Upon h-normal \Gamma-linear connections on J^1(T,M) (original) (raw)
Related papers
Ricci and Bianchi identities for h-normal Γ-linear connections on J1(T,M)
International Journal of Mathematics and Mathematical Sciences, 2003
The aim of this paper is to describe the local Ricci and Bianchi identities of an hnormal Γ -linear connection on the first-order jet fibre bundle J 1 (T , M). We present the physical and geometrical motives that determined our study and introduce the h-normal Γ -linear connections on J 1 (T , M), emphasizing their particular local features. We describe the expressions of the local components of torsion and curvature d-tensors produced by an h-normal Γ -linear connection ∇Γ , and analyze the local Ricci identities induced by ∇Γ , together with their derived local deflection d-tensors identities. Finally, we expose the local expressions of Bianchi identities which geometrically connect the local torsion and curvature d-tensors of connection ∇Γ .
In this paper we describe the local Ricci and Bianchi identities for an h-normal N-linear connection D\Gamma(N) on the dual 1-jet space J^{1*}(T,M). To reach this aim, we firstly give the expressions of the local distinguished (d-) adapted components of torsion and curvature tensors produced by D\Gamma(N), and then we analyze their attached local Ricci identities. The derived deflection d-tensor identities are also presented. Finally, we expose the local expressions of the Bianchi identities (in the particular case of an h-normal N-linear connection of Cartan type), which geometrically connect the local torsion and curvature d-tensors of the linear connection D\Gamma(N).
Upon H-normal Γ-linear Connections on J
2000
Section 1 introduces the notion of h-normal Γ-linear connection on the 1-jet fibre bundle J(T, M), and studies its local components. Section 2 analyses the main local components of torsion and curvature d-tensors attached to an h-normal Γ-linear connection ∇. Section 3 presents the local Ricci identities induced by ∇. The identities of the local deflection d-tensors are also exposed. Section 4 is dedicated to the writing of the local Bianchi identities of ∇. Mathematics Subject Classification (1991): 53C07, 53C43, 53C99.
Upon h-normal Γ-linear connections on J ^1 ( T , M )
2000
Section 1 introduces the notion of h-normal Γ-linear connection on the 1-jet fibre bundle J(T, M) and studies its torsion and curvature d-tensors. Section 2 is dedicated to the writing of the Ricci and Bianchi identities of a h-normal Γ-linear connection ∇. At the same time, Section 2 presents the important deflection tensor identities extremely used in the construction of the subsequent Maxwell equations of the electromagnetic field on the 1-jet space [3], [4]. Mathematics Subject Classification: 53C07, 53C43, 53C99.
Torsions and Curvatures on Jet Fibre Bundle J^1(T,M)
The aim of this paper is twofold. On the one hand, to study the local representations of d-connections, d-torsions and d-curvatures with respect to adapted bases produced by a nonlinear connection Γ on the jet fibre bundle of order one J 1 (T, M ) → T × M . On the other hand, to open the problem of prolongations of tensors and connections from a product of two manifolds to 1-jet fibre bundle associated to these manifolds.
The local description of the Ricci and Bianchi
2011
In this paper we describe the local Ricci and Bianchi identities for an hnormal N-linear connection DΓ(N) on the dual 1-jet space J 1 * (T , M). To reach this aim, we firstly give the expressions of the local distinguished (d-) adapted components of torsion and curvature tensors produced by DΓ(N), and then we analyze their attached local Ricci identities. The derived deflection d-tensor identities are also presented. Finally, we expose the local expressions of the Bianchi identities (in the particular case of an hnormal N-linear connection of Cartan type), which geometrically connect the local torsion and curvature d-tensors of the linear connection DΓ(N).
Torsion, Curvature and Deflection d-Tensors on J^1(T,M)
Balkan Journal of Geometry and Its Applications, 2001
The paper introduces the notion of \Gamma-linear connection \nabla on the -jet fibre bundle J^1(T,M), and presents its local components. We also describe the local Ricci and Bianchi identities of nabla\nablanabla.
d-Metrics and Nonlinear Connections on 1-Jet Fibre Bundles
2003
The aim of this paper is to open the problem of construction of a nonlinear connection Gamma=(M(i)(alpha)beta,N(i)(alpha)j)\Gamma=(M^{(i)}_{(\alpha)\beta}, N^{(i)}_{(\alpha)j})Gamma=(M(i)(alpha)beta,N(i)(alpha)j) on the jet bundle of first order J1(T,M)J^1(T,M)J1(T,M), which to be canonically produced by a Kronecker product vertical metrical d-tensor G(alpha)(beta)(i)(j)=halphabetagijG^{(\alpha)(\beta)}_{(i)(j)}=h^{\alpha\beta}g_{ij}G(alpha)(beta)(i)(j)=halphabetagij, possibly provided by multi-time dependent quadratic Lagrangians coming from various branches of theoretical physics: bosonic strings theory, electrodynamics or elasticity.
Torsion and Ricci tensor for non-linear connections
Differential Geometry and its Applications, 1991
We study a natural generalization of the concepts of torsion and Ricci tensor for a nonlinear connection on a fibred manifolds, with respect to a given fibred soldering form. Our results are achieved by means of the differentials and codifferentials induced by the Frölicher-Nijenhuis graded Lie algebra of tangent valued forms.