Vladimir Ivashchuk - Academia.edu (original) (raw)

Papers by Vladimir Ivashchuk

A multidimensional cosmological model with space-time consisting of n(n ≥ 2) Ein-stein spaces M i... more A multidimensional cosmological model with space-time consisting of n(n ≥ 2) Ein-stein spaces M i is investigated in the presence of a cosmological constant Λ and a homogeneous minimally coupled scalar field ϕ(t) as a matter source. Classical and quantum wormhole solutions are obtained for Λ < 0 and all M i being Ricci-flat. Classical wormhole solutions are also found for Λ < 0 and only one of the M i being Ricci-flat for the case of spontaneous compactification of the internal dimensions with fine tuning of parameters.

Gravitation and Cosmology, 2010

A multidimensional cosmological type model with 1-component anisotropic fluid is considered. An e... more A multidimensional cosmological type model with 1-component anisotropic fluid is considered. An exact solution is obtained. This solution is defined on a product manifold containing n Ricci-flat factor spaces. We singled out a special solution governed by the function cosh . It is shown that this special solution has Kasner-like asymptotics in the limits τ → +0 and τ → +∞ , where τ is a synchronous time variable. A relation between two sets of Kasner parameters α ∞ and α 0 is found. This formula (of "scattering law") is coinciding with that obtained earlier for the S -brane solution (when scalar fields are absent).

The Tenth Marcel Grossmann Meeting, 2006

A family of generalized S-brane solutions with orthogonal intersection rules and n Ricci-flat fac... more A family of generalized S-brane solutions with orthogonal intersection rules and n Ricci-flat factor spaces in the theory with several scalar fields, antisymmetric forms and multiple scalar potential is considered. Two subclasses of solutions with power-law and exponential behaviour of scale factors are singled out. These subclasses contain sub-families of solutions with accelerated expansion of certain factor spaces. Some examples of solutions with exponential dependence of one scale factor and constant scale factors of "internal" spaces (e.g. Freund-Rubin type solutions) are also considered.

Lecture Notes in Physics, 2000

Multidimensional model describing the "cosmological" and/ or spherically symmetric configuration ... more Multidimensional model describing the "cosmological" and/ or spherically symmetric configuration with (n + 1) Einstein spaces in the theory with several scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, n "internal" spaces are Ricci-flat, one space M 0 has a non-zero curvature, and all p-branes do not "live" in M 0 , a class of exact solutions is obtained if certain block-orthogonality relations on p-brane vectors are imposed. A subclass of spherically-symmetric solutions containing non-extremal p-brane black holes is considered. Post-Newtonian parameters are calculated and some examples are considered. This means that either the limit of terrestrial accuracies is reached or we have some new physics entering the measurement procedure . First means that we should shift to space experiments to measure G [15] and second means that more thorough study of theories generalizing Einstein's general relativity is necessary.

AIP Conference Proceedings, 2007

Main results in obtaining exact solutions for multidimensional models and their application to so... more Main results in obtaining exact solutions for multidimensional models and their application to solving main problems of modern cosmology and black hole physics are described. Some new results on composite fluxbrane and S-brane solutions for a wide class of intersection rules are presented. These solutions are defined on a product manifold R&amp;amp;ast; × M1 × &amp;amp;ellip; × Mn which contains n Ricci-flat spaces M1,&amp;amp;ellip;,Mn with 1-dimensional R&amp;amp;ast; and M1. They are defined up to a set of functions obeying non-linear differential equations equivalent to Toda-type equations with certain boundary conditions imposed. Exact solutions corresponding to configurations with two branes and intersections related to simple Lie algebras C2 and G2 are obtained. In these cases the functions Hs(z), s = 1, 2, are polynomials of degrees: (3, 4) and (6, 10), respectively, in agreement with a conjecture suggested earlier. Examples of simple S-brane solutions describing an accelerated expansion of a certain factor-space are given explicitely.

International Journal of Modern Physics D, 1995

The n-time generalization of Schwarzschild solution is presented. The equations of geodesics for ... more The n-time generalization of Schwarzschild solution is presented. The equations of geodesics for the metric are integrated and the motion of the relativistic particle is considered. The multitemporal analogue of the Newton's gravitational law for the objects, described by the solution, is suggested. The scalar-vacuum generalization of the multitemporal solution is also presented.

Exact solutions with an exponential behaviour of the scale factors are considered in a multidimen... more Exact solutions with an exponential behaviour of the scale factors are considered in a multidimensional cosmological model describing the dynamics of n+1 Ricci-flat factor spaces M_i in the presence of a one-component perfect fluid. The pressures in all spaces are proportional to the density: p_i = w_i \rho, i = 0,...,n. Solutions with accelerated expansion of our 3-space M_0 and

Gravitation and Cosmology, Sep 1, 2001

A (1 + d)-dimensional thick "brane world" model with varying Lambda-term is considered. The model... more A (1 + d)-dimensional thick "brane world" model with varying Lambda-term is considered. The model is generalized to the case of a chain of Ricci-flat internal spaces when the matter source is an anisotropic perfect fluid. The "horizontal" part of potential is obtained in the Newtonian approximation. In the multitemporal case (with a Lambda-term) a set of equations for potentials is presented.

The Chaotic Universe, 2000

Cosmological model describing the evolution of n Einstein spaces in the theory with l scalar fiel... more Cosmological model describing the evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When electro-magnetic composite pbrane ansatz is adopted, and certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity is reduced to a billiard on the (N -1)-dimensional Lobachevsky space HN-1, N = n +l. The geometrical criterion for the finiteness of the billiard volume and its compactness is used. This criterion reduces the problem to the problem of illumination of a sphere SN-2 by point-like sources. Some examples with billiards of finite volume and hence oscillating behaviour near the singularity are considered. Among them examples with square and triangle 2-dimensional billiards (e.g. that of the Bianchi-IX model) and a 4-dimensional billiard in "truncated" D = 11 supergravity model are considered.

Gravit Cosmol, 2003

A family of spherically symmetric solutions in the model with 1-component anisotropic fluid is co... more A family of spherically symmetric solutions in the model with 1-component anisotropic fluid is considered. The metric of the solution depends on a parameter q > 0 relating radial pressure and the density and contains n -1 parameters corresponding to Ricci-flat ``internal space'' metrics. For q = 1 and certain equations of state the metric coincides with the metric of black brane solutions in the model with antisymmetric form. A family of black hole solutions corresponding to natural numbers q = 1,2, ... is singled out. Certain examples of solutions (e.g. containing for q =1 Reissner-Nordstr\"{o}m, M2 and M5 black brane metrics) are considered. The post-Newtonian parameters beta and gamma corresponding to the 4-dimensional section of the metric are calculated.

Gravitation and Cosmology, Oct 14, 2006

In this paper we generalize electric S-brane solutions with maximal number of branes. Previously ... more In this paper we generalize electric S-brane solutions with maximal number of branes. Previously for the action containing D-dimensional gravity, a scalar field and antisymmetric (p+2)-form we found composite, electric S-brane solutions with all non-zero ``charge'' densities which obeyed self-duality or anti-self-duality relations. These solutions occurred when D = 4m+1 = 5, 9, 13, >... and p = 2m-1 = 1, 3, 5, ... Here we generalize these solutions to the case when the spatial 4m-dimensional submanifold is Ricci-flat rather than simply Euclidean-flat and the charge density form is a parallel self-dual or anti-self-dual form of rank 2m. Also generalizations are found for the case when there is an extra ``internal'' Ricci-flat manifold not covered by the S-branes. In the case when one allows a phantom scalar field a subset of these solutions lead to accelerated expansion of this extra spatial factor space not covered by the S-branes while the other spatial factor space of dimension 4m contracts. Some of these S-brane solutions also provide specific examples of solutions of type IIA supergravity.

Multidimensional cosmological-type model with n Einstein factor spaces in the theory with l scala... more Multidimensional cosmological-type model with n Einstein factor spaces in the theory with l scalar fields and multiple exponential potential is considered. The dynamics of the model near the singularity is reduced to a billiard on the (N − 1)-dimensional Lobachevsky space H N −1 , N = n + l. It is shown that for n > 1 the oscillating behaviour near the singularity is absent and solutions have an asymptotical Kasner-like behavior. For the case of one scale factor (n = 1) billiards with finite volumes (e.g. coinciding with that of the Bianchi-IX model) are described and oscillating behaviour of scalar fields near the singularity is obtained.

In this paper we consider (n+1)(n+1)(n+1)-dimensional cosmological model with scalar field and antisymmet... more In this paper we consider (n+1)(n+1)(n+1)-dimensional cosmological model with scalar field and antisymmetric (p+2)(p+2)(p+2)-form. Using an electric composite SpSpSp-brane ansatz the field equations for the original system reduce to the equations for a Toda-like system with n(n−1)/2n(n-1)/2n(n−1)/2 quadratic constraints on the charge densities. For certain odd dimensions ($D = 4m+1 = 5, 9, 13, ...$) and (p+2)(p+2)(p+2)-forms ($p = 2m-1 = 1, 3, 5, ...$) these algebraic constraints can be satisfied with the maximal number of charged branes (i.e.} all the branes have non-zero charge densities). These solutions are characterized by self-dual or anti-self-dual charge density forms QQQ (of rank 2m2m2m). For these algebraic solutions with the particular DDD, ppp, QQQ and non-exceptional dilatonic coupling constant lambda\lambdalambda we obtain general cosmological solutions to the field equations and some properties of these solutions are examined. In particuilar Kasner-like behavior, the existence of attractor solutions.

Regular and Chaotic Dynamics, Nov 1, 2008

The pseudo-Euclidean Toda-like system of cosmological origin is considered. When certain restrict... more The pseudo-Euclidean Toda-like system of cosmological origin is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the ``singularity'' is reduced to a billiard on the (n-1)-dimensional Lobachevsky space H^{n-1}. The geometrical criterion for the finiteness of the billiard volume and its compactness is suggested. This criterion reduces the problem to the problem of illumination of (n-2)-dimensional sphere S^{n-2} by point-like sources. Some examples are considered.

Gravitation and Cosmology, Mar 31, 1995

A cosmological model describing the evolution of n Ricci-flat spaces (n>1) in the presence of 1-c... more A cosmological model describing the evolution of n Ricci-flat spaces (n>1) in the presence of 1-component perfect-fluid and minimally coupled scalar field is considered. When the pressures in all spaces are proportional to the density, the Einstein and Wheeler-DeWitt equations are integrated for a large variety of parameters. Classical and quantum wormhole solutions are obtained for negative density. Some special classes of solutions, e.g. solutions with spontaneous and dynamical compactification, exponential and power-law inflations, are singled out. For positive density a third quantized cosmological model is considered and the Planckian spectrum of ``created universes'' is obtained.

Gravit Cosmol, 2000

Black hole p-brane solutions for a wide class of intersection rules are considered. The solutions... more Black hole p-brane solutions for a wide class of intersection rules are considered. The solutions are defined on a manifold which contains a product of n-1 Ricci-flat "internal'' spaces. The post-Newtonian parameters "beta" and "gamma" corresponding to a 4-dimensional section of the metric for general intersection rules are studied. It is shown that "beta" does not depend but "gamma" depends on brane intersections. For "block-orthogonal" intersection rules spherically symmetric solutions are considered, and explicit relations for post-Newtonian parameters are obtained. The bounds on parameters of solutions following from observational restrictions in the Solar system are presented.

Phys Lett B, 1997

Multidimensional gravitational model on the manifold M = M0 × ∏i=1nMi, where Mi are Einstein spac... more Multidimensional gravitational model on the manifold M = M0 × ∏i=1nMi, where Mi are Einstein spaces (i ≥ 1), is considered. The action contains m = 2n − 1 dilatonic scalar fields ϕ1 and m (antisymmetric) forms A1. When all fields and scale factors of the metric depend (essentially) on the point of M0 and any A1 is “proportional” to

Phys Lett B, 1997

Multidimensional gravitational model on the manifold M = M0 × Πni=1Mi are Einstein spaces (i >= 1... more Multidimensional gravitational model on the manifold M = M0 × Πni=1Mi are Einstein spaces (i >= 1), is considered. The action contains m = 2n - 1 dilatonic scalar fields ϕI and m (antisymmetric) forms AI. When all fields and scale factors of the metric depend (essentially) on the point of M0 and any AI is ``proportional'' to the volume form of submanifold Mi1 × ... × Mik, 1 <= i1 < ... < ik <= n, the σ-model representation is obtained. A family of ``Majumdar-Papapetrou type'' solutions are obtained, when all Mv are Ricci-flat. Relation of our generalized p-branes to usual intersecting p-branes is discussed.

A multidimensional cosmological model with space-time consisting of n(n ≥ 2) Ein-stein spaces M i... more A multidimensional cosmological model with space-time consisting of n(n ≥ 2) Ein-stein spaces M i is investigated in the presence of a cosmological constant Λ and a homogeneous minimally coupled scalar field ϕ(t) as a matter source. Classical and quantum wormhole solutions are obtained for Λ < 0 and all M i being Ricci-flat. Classical wormhole solutions are also found for Λ < 0 and only one of the M i being Ricci-flat for the case of spontaneous compactification of the internal dimensions with fine tuning of parameters.

Gravitation and Cosmology, 2010

A multidimensional cosmological type model with 1-component anisotropic fluid is considered. An e... more A multidimensional cosmological type model with 1-component anisotropic fluid is considered. An exact solution is obtained. This solution is defined on a product manifold containing n Ricci-flat factor spaces. We singled out a special solution governed by the function cosh . It is shown that this special solution has Kasner-like asymptotics in the limits τ → +0 and τ → +∞ , where τ is a synchronous time variable. A relation between two sets of Kasner parameters α ∞ and α 0 is found. This formula (of "scattering law") is coinciding with that obtained earlier for the S -brane solution (when scalar fields are absent).

The Tenth Marcel Grossmann Meeting, 2006

A family of generalized S-brane solutions with orthogonal intersection rules and n Ricci-flat fac... more A family of generalized S-brane solutions with orthogonal intersection rules and n Ricci-flat factor spaces in the theory with several scalar fields, antisymmetric forms and multiple scalar potential is considered. Two subclasses of solutions with power-law and exponential behaviour of scale factors are singled out. These subclasses contain sub-families of solutions with accelerated expansion of certain factor spaces. Some examples of solutions with exponential dependence of one scale factor and constant scale factors of "internal" spaces (e.g. Freund-Rubin type solutions) are also considered.

Lecture Notes in Physics, 2000

Multidimensional model describing the "cosmological" and/ or spherically symmetric configuration ... more Multidimensional model describing the "cosmological" and/ or spherically symmetric configuration with (n + 1) Einstein spaces in the theory with several scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, n "internal" spaces are Ricci-flat, one space M 0 has a non-zero curvature, and all p-branes do not "live" in M 0 , a class of exact solutions is obtained if certain block-orthogonality relations on p-brane vectors are imposed. A subclass of spherically-symmetric solutions containing non-extremal p-brane black holes is considered. Post-Newtonian parameters are calculated and some examples are considered. This means that either the limit of terrestrial accuracies is reached or we have some new physics entering the measurement procedure . First means that we should shift to space experiments to measure G [15] and second means that more thorough study of theories generalizing Einstein's general relativity is necessary.

AIP Conference Proceedings, 2007

Main results in obtaining exact solutions for multidimensional models and their application to so... more Main results in obtaining exact solutions for multidimensional models and their application to solving main problems of modern cosmology and black hole physics are described. Some new results on composite fluxbrane and S-brane solutions for a wide class of intersection rules are presented. These solutions are defined on a product manifold R&amp;amp;ast; × M1 × &amp;amp;ellip; × Mn which contains n Ricci-flat spaces M1,&amp;amp;ellip;,Mn with 1-dimensional R&amp;amp;ast; and M1. They are defined up to a set of functions obeying non-linear differential equations equivalent to Toda-type equations with certain boundary conditions imposed. Exact solutions corresponding to configurations with two branes and intersections related to simple Lie algebras C2 and G2 are obtained. In these cases the functions Hs(z), s = 1, 2, are polynomials of degrees: (3, 4) and (6, 10), respectively, in agreement with a conjecture suggested earlier. Examples of simple S-brane solutions describing an accelerated expansion of a certain factor-space are given explicitely.

International Journal of Modern Physics D, 1995

The n-time generalization of Schwarzschild solution is presented. The equations of geodesics for ... more The n-time generalization of Schwarzschild solution is presented. The equations of geodesics for the metric are integrated and the motion of the relativistic particle is considered. The multitemporal analogue of the Newton's gravitational law for the objects, described by the solution, is suggested. The scalar-vacuum generalization of the multitemporal solution is also presented.

Exact solutions with an exponential behaviour of the scale factors are considered in a multidimen... more Exact solutions with an exponential behaviour of the scale factors are considered in a multidimensional cosmological model describing the dynamics of n+1 Ricci-flat factor spaces M_i in the presence of a one-component perfect fluid. The pressures in all spaces are proportional to the density: p_i = w_i \rho, i = 0,...,n. Solutions with accelerated expansion of our 3-space M_0 and

Gravitation and Cosmology, Sep 1, 2001

A (1 + d)-dimensional thick "brane world" model with varying Lambda-term is considered. The model... more A (1 + d)-dimensional thick "brane world" model with varying Lambda-term is considered. The model is generalized to the case of a chain of Ricci-flat internal spaces when the matter source is an anisotropic perfect fluid. The "horizontal" part of potential is obtained in the Newtonian approximation. In the multitemporal case (with a Lambda-term) a set of equations for potentials is presented.

The Chaotic Universe, 2000

Cosmological model describing the evolution of n Einstein spaces in the theory with l scalar fiel... more Cosmological model describing the evolution of n Einstein spaces in the theory with l scalar fields and forms is considered. When electro-magnetic composite pbrane ansatz is adopted, and certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity is reduced to a billiard on the (N -1)-dimensional Lobachevsky space HN-1, N = n +l. The geometrical criterion for the finiteness of the billiard volume and its compactness is used. This criterion reduces the problem to the problem of illumination of a sphere SN-2 by point-like sources. Some examples with billiards of finite volume and hence oscillating behaviour near the singularity are considered. Among them examples with square and triangle 2-dimensional billiards (e.g. that of the Bianchi-IX model) and a 4-dimensional billiard in "truncated" D = 11 supergravity model are considered.

Gravit Cosmol, 2003

A family of spherically symmetric solutions in the model with 1-component anisotropic fluid is co... more A family of spherically symmetric solutions in the model with 1-component anisotropic fluid is considered. The metric of the solution depends on a parameter q > 0 relating radial pressure and the density and contains n -1 parameters corresponding to Ricci-flat ``internal space'' metrics. For q = 1 and certain equations of state the metric coincides with the metric of black brane solutions in the model with antisymmetric form. A family of black hole solutions corresponding to natural numbers q = 1,2, ... is singled out. Certain examples of solutions (e.g. containing for q =1 Reissner-Nordstr\"{o}m, M2 and M5 black brane metrics) are considered. The post-Newtonian parameters beta and gamma corresponding to the 4-dimensional section of the metric are calculated.

Gravitation and Cosmology, Oct 14, 2006

In this paper we generalize electric S-brane solutions with maximal number of branes. Previously ... more In this paper we generalize electric S-brane solutions with maximal number of branes. Previously for the action containing D-dimensional gravity, a scalar field and antisymmetric (p+2)-form we found composite, electric S-brane solutions with all non-zero ``charge'' densities which obeyed self-duality or anti-self-duality relations. These solutions occurred when D = 4m+1 = 5, 9, 13, >... and p = 2m-1 = 1, 3, 5, ... Here we generalize these solutions to the case when the spatial 4m-dimensional submanifold is Ricci-flat rather than simply Euclidean-flat and the charge density form is a parallel self-dual or anti-self-dual form of rank 2m. Also generalizations are found for the case when there is an extra ``internal'' Ricci-flat manifold not covered by the S-branes. In the case when one allows a phantom scalar field a subset of these solutions lead to accelerated expansion of this extra spatial factor space not covered by the S-branes while the other spatial factor space of dimension 4m contracts. Some of these S-brane solutions also provide specific examples of solutions of type IIA supergravity.

Multidimensional cosmological-type model with n Einstein factor spaces in the theory with l scala... more Multidimensional cosmological-type model with n Einstein factor spaces in the theory with l scalar fields and multiple exponential potential is considered. The dynamics of the model near the singularity is reduced to a billiard on the (N − 1)-dimensional Lobachevsky space H N −1 , N = n + l. It is shown that for n > 1 the oscillating behaviour near the singularity is absent and solutions have an asymptotical Kasner-like behavior. For the case of one scale factor (n = 1) billiards with finite volumes (e.g. coinciding with that of the Bianchi-IX model) are described and oscillating behaviour of scalar fields near the singularity is obtained.

In this paper we consider (n+1)(n+1)(n+1)-dimensional cosmological model with scalar field and antisymmet... more In this paper we consider (n+1)(n+1)(n+1)-dimensional cosmological model with scalar field and antisymmetric (p+2)(p+2)(p+2)-form. Using an electric composite SpSpSp-brane ansatz the field equations for the original system reduce to the equations for a Toda-like system with n(n−1)/2n(n-1)/2n(n−1)/2 quadratic constraints on the charge densities. For certain odd dimensions ($D = 4m+1 = 5, 9, 13, ...$) and (p+2)(p+2)(p+2)-forms ($p = 2m-1 = 1, 3, 5, ...$) these algebraic constraints can be satisfied with the maximal number of charged branes (i.e.} all the branes have non-zero charge densities). These solutions are characterized by self-dual or anti-self-dual charge density forms QQQ (of rank 2m2m2m). For these algebraic solutions with the particular DDD, ppp, QQQ and non-exceptional dilatonic coupling constant lambda\lambdalambda we obtain general cosmological solutions to the field equations and some properties of these solutions are examined. In particuilar Kasner-like behavior, the existence of attractor solutions.

Regular and Chaotic Dynamics, Nov 1, 2008

The pseudo-Euclidean Toda-like system of cosmological origin is considered. When certain restrict... more The pseudo-Euclidean Toda-like system of cosmological origin is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the ``singularity'' is reduced to a billiard on the (n-1)-dimensional Lobachevsky space H^{n-1}. The geometrical criterion for the finiteness of the billiard volume and its compactness is suggested. This criterion reduces the problem to the problem of illumination of (n-2)-dimensional sphere S^{n-2} by point-like sources. Some examples are considered.

Gravitation and Cosmology, Mar 31, 1995

A cosmological model describing the evolution of n Ricci-flat spaces (n>1) in the presence of 1-c... more A cosmological model describing the evolution of n Ricci-flat spaces (n>1) in the presence of 1-component perfect-fluid and minimally coupled scalar field is considered. When the pressures in all spaces are proportional to the density, the Einstein and Wheeler-DeWitt equations are integrated for a large variety of parameters. Classical and quantum wormhole solutions are obtained for negative density. Some special classes of solutions, e.g. solutions with spontaneous and dynamical compactification, exponential and power-law inflations, are singled out. For positive density a third quantized cosmological model is considered and the Planckian spectrum of ``created universes'' is obtained.

Gravit Cosmol, 2000

Black hole p-brane solutions for a wide class of intersection rules are considered. The solutions... more Black hole p-brane solutions for a wide class of intersection rules are considered. The solutions are defined on a manifold which contains a product of n-1 Ricci-flat "internal'' spaces. The post-Newtonian parameters "beta" and "gamma" corresponding to a 4-dimensional section of the metric for general intersection rules are studied. It is shown that "beta" does not depend but "gamma" depends on brane intersections. For "block-orthogonal" intersection rules spherically symmetric solutions are considered, and explicit relations for post-Newtonian parameters are obtained. The bounds on parameters of solutions following from observational restrictions in the Solar system are presented.

Phys Lett B, 1997

Multidimensional gravitational model on the manifold M = M0 × ∏i=1nMi, where Mi are Einstein spac... more Multidimensional gravitational model on the manifold M = M0 × ∏i=1nMi, where Mi are Einstein spaces (i ≥ 1), is considered. The action contains m = 2n − 1 dilatonic scalar fields ϕ1 and m (antisymmetric) forms A1. When all fields and scale factors of the metric depend (essentially) on the point of M0 and any A1 is “proportional” to

Phys Lett B, 1997

Multidimensional gravitational model on the manifold M = M0 × Πni=1Mi are Einstein spaces (i >= 1... more Multidimensional gravitational model on the manifold M = M0 × Πni=1Mi are Einstein spaces (i >= 1), is considered. The action contains m = 2n - 1 dilatonic scalar fields ϕI and m (antisymmetric) forms AI. When all fields and scale factors of the metric depend (essentially) on the point of M0 and any AI is ``proportional'' to the volume form of submanifold Mi1 × ... × Mik, 1 <= i1 < ... < ik <= n, the σ-model representation is obtained. A family of ``Majumdar-Papapetrou type'' solutions are obtained, when all Mv are Ricci-flat. Relation of our generalized p-branes to usual intersecting p-branes is discussed.