EROL KILIÇ - Academia.edu (original) (raw)

Papers by EROL KILIÇ

Research paper thumbnail of Hypersurfaces of Lorentzian para-Sasakian manifolds

arXiv (Cornell University), Sep 25, 2009

Research paper thumbnail of Biharmonic Curves in 3-dimensional Hyperbolic Heisenberg Group

arXiv (Cornell University), Mar 3, 2011

Research paper thumbnail of The pedal of hypersurface with a constant support function

The locus of the foot of the perpendicular from a point O to a tangent hyperplane of a given hype... more The locus of the foot of the perpendicular from a point O to a tangent hyperplane of a given hypersurface M in Euclidean space E n+1 is called the pedal of M with respect to O. Applications of the pedal in differential geometry can be found in papers by Th. Hasanis and D. Koutroufiotis [J. Geom. 24, 131-167 (1985; Zbl 0578.53002)], Chr. Georgiou, Th. Hasanis and D. Koutroufiotis [Geom. Dedicata 28, 153-169 (1988; Zbl 0659.53004)]. In the paper under review, the authors try to study the differential geometry of the pedal of a hypersurface with a constant support function. The study is trivial since in that case the pedal is a hypersphere. Euclidean hypersurfaces with a constant support function have been classified by Th. Hasanis and D. Koutroufiotis [Arch. Math. 57, 189-192 (1991; Zbl 0697.53012)].

Research paper thumbnail of Biharmonic Hypersurfaces of Lorentzian Para-Sasakian Manifolds

Research paper thumbnail of On A Semi-Symmetric On Non-Metric Connection In An Lp-Sasakian Manifold

International electronic journal of geometry, Oct 30, 2010

Research paper thumbnail of On a Semi-Symmetric Non-Metric Connection in an LP-Sasakian Manifold

Research paper thumbnail of Einstein like (epsilon)-para Sasakian manifolds

Research paper thumbnail of Curves Assocıated with an M Vector Field on a Semi Riemannian Hypersurface M of a Lorentzian Manifold M

Research paper thumbnail of The Stability Problem of Certain Anti-Invariant Submanifolds in Golden Riemannian Manifolds

International electronic journal of geometry, Apr 30, 2023

In this study, we discuss the stability of some anti-invariant submanifolds of golden Riemannian ... more In this study, we discuss the stability of some anti-invariant submanifolds of golden Riemannian manifolds under certain conditions in terms of the Ricci curvature tensors of the ambient manifold and the submanifold.

Research paper thumbnail of Einstein Metrics Induced by Natural Riemann Extensions

Advances in Applied Clifford Algebras, Mar 21, 2017

Clifford algebras are used in theoretical physics and in particular, in the general theory of rel... more Clifford algebras are used in theoretical physics and in particular, in the general theory of relativity, where Einstein's equations are rewritten in Girard (Adv Appl Clifford Algebras 9(2):225-230, 1999) within a Clifford algebra. Let M be a manifold with a torsion-free connection which induces on its cotangent bundle T * M , a semi-Riemannian metricḡ, called the natural Riemann extension, Kowalski and Sekizawa (Publ Math Debrecen 78:709-721, 2011). The main result of the present paper gives a necessary and sufficient condition forḡ restricted to certain hypersurfaces of T * M to be Einstein.

Research paper thumbnail of On Invariant Submanifolds of Riemannian Warped Product Manifold

Turkish Journal of Mathematics, Mar 1, 2003

In this paper, we generalize the geometry of the invariant submanifolds of Riemannian product man... more In this paper, we generalize the geometry of the invariant submanifolds of Riemannian product manifold to the geometry of the invariant submanifolds of Riemannian warped product manifold. We investigate some properties of an invariant submanifolds of a Riemannian warped product manifold. We show that every invariant submanifold of the Riemannian warped product manifold is a Riemannian warped product manifold. Also, we give a theorem on the pseudo-umbilical invariant submanifold. Further, we obtain that integral manifolds on an invariant submanifold are curvature-invariant submanifolds. Finally, we give a necessary condititon on a totally umbilical invariant submanifold to be totally geodesic.

Research paper thumbnail of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:msub><mml:mrow><mml:mo st...

Journal of Geometry and Physics, Nov 1, 2021

Abstract In this paper, we define and study two new structures on a differentiable manifold calle... more Abstract In this paper, we define and study two new structures on a differentiable manifold called by us an f ( a , b ) ( 3 , 2 , 1 ) -structure and a framed f ( a , b ) ( 3 , 2 , 1 ) -structure as a generalization of some geometric structures determined by polynomial structures, where a , b ∈ R and b ≠ 0 . At beginning, we present some examples regarding f ( a , b ) ( 3 , 2 , 1 ) -structures and establish their some fundamental properties. We also give a necessary condition for an f ( a , b ) ( 3 , 2 , 1 ) -structure to be an almost quadratic ϕ-structure. Later, it is shown that the existence of two semi-Riemannian metrics on differentiable manifolds admitting a framed f ( a , b ) ( 3 , 2 , 1 ) -structure, i.e., framed f ( a , b ) ( 3 , 2 , 1 ) -manifolds. In particular, a framed f ( a , b ) ( 3 , 2 , 1 ) -manifold endowed with the first semi-Riemannian metric mentioned above is called a framed metric f ( a , b ) ( 3 , 2 , 1 ) -manifold. Finally, we construct some examples to illustrate the existence of framed metric f ( a , b ) ( 3 , 2 , 1 ) -manifolds.

Research paper thumbnail of On Lightlike Hypersurfaces of a Semi-Riemannian Space form

DergiPark (Istanbul University), Feb 1, 2003

In this paper, we study a Lightlike hypersurface of a semi-Riemann manifold. We show that a light... more In this paper, we study a Lightlike hypersurface of a semi-Riemann manifold. We show that a lightlike hypersurface is totally geodesic if and only if it is locally symmetric. Also, we show that a lightlike Hypersurface of IR 4m 4q (m, q > 1) is totally geodesic under some restrictions. Finally, we give some results on Ricci curvature of a lightlike hypersurface to be symmetric.

Research paper thumbnail of Chen invariants for Riemannian submersions and their applications in meteorology

arXiv (Cornell University), Feb 17, 2017

In this paper, an optimal inequality involving the delta curvature is exposed. An application of ... more In this paper, an optimal inequality involving the delta curvature is exposed. An application of Riemannian submersions dealing meteorology is presented. Some characterizations about the vertical motion and the horizontal divergence are obtained.

Research paper thumbnail of Ricci Soliton Lightlike Submanifolds with Co-Dimension <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2</span></span></span></span>

Fundamental journal of mathematics and applications, Jun 30, 2023

The necessary requirements for half-lightlike and coisotropic lightlike submanifolds to be a Ricc... more The necessary requirements for half-lightlike and coisotropic lightlike submanifolds to be a Ricci soliton are obtained. Some examples of Ricci soliton half-lightlike and Ricci soliton coisotropic lightlike submanifolds are given. The Ricci soliton equation is investigated on totally geodesic, totally umbilical, and irrotational lightlike submanifolds.

Research paper thumbnail of Legendre Curves on Generalized Paracontact Metric Manifolds

Bulletin of the Malaysian Mathematical Sciences Society, Mar 1, 2017

Two different notions of almost paracontact structures (which are compatible or anti-compatible w... more Two different notions of almost paracontact structures (which are compatible or anti-compatible with the metric), well known in the literature, are unified and generalized here. Several formulas of paraholomorphic maps are established, and a result of Lichnerowicz type is obtained. The connection transformations which have the same system of paracontact-planar Legendre curves are characterized. Conformal changes of metrics which preserve geodesics (resp. paracontact-planar Legendre curves) are studied.

Research paper thumbnail of Totally umbilical semi-invariant submanifolds in locally decomposable metallic Riemannian manifolds

Filomat

In this paper, we obtain some classification theorems for totally umbilical semi-invariant subman... more In this paper, we obtain some classification theorems for totally umbilical semi-invariant submanifolds in locally decomposable metallic Riemannian manifolds. We also prove that there exist no totally umbilical proper semi-invariant submanifolds in a posivitely or negatively curved locally decomposable metallic Riemannian manifold

Research paper thumbnail of Some characterizations on indefinite space forms admitting almost contact structures

Asian-European Journal of Mathematics

In this paper, the projective curvature tensor field of a generalized indefinite Sasakian space f... more In this paper, the projective curvature tensor field of a generalized indefinite Sasakian space form is investigated. Some results dealing with projectively semi-symmetric and [Formula: see text]-projectively semi-symmetric generalized indefinite Sasakian space forms are obtained. Furthermore, biharmonic Legendre Frenet curves are discussed on these manifolds.

Research paper thumbnail of Hypersurfaces of LP-Sasakian manifolds

arXiv: Differential Geometry, 2009

In this paper, we study the invariant and non-invariant hypersurfaces of (1,1)(1,1)(1,1) almost contact m... more In this paper, we study the invariant and non-invariant hypersurfaces of (1,1)(1,1)(1,1) almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively.

Research paper thumbnail of Inequalities for scalar curvature of pseudo-Riemannian submanifolds

Journal of Geometry and Physics, 2017

Abstract Some basic inequalities, involving the scalar curvature and the mean curvature, for a ps... more Abstract Some basic inequalities, involving the scalar curvature and the mean curvature, for a pseudo-Riemannian submanifold of a pseudo-Riemannian manifold are obtained. We also find inequalities for spacelike submanifolds. Equality cases are also discussed.

Research paper thumbnail of Hypersurfaces of Lorentzian para-Sasakian manifolds

arXiv (Cornell University), Sep 25, 2009

Research paper thumbnail of Biharmonic Curves in 3-dimensional Hyperbolic Heisenberg Group

arXiv (Cornell University), Mar 3, 2011

Research paper thumbnail of The pedal of hypersurface with a constant support function

The locus of the foot of the perpendicular from a point O to a tangent hyperplane of a given hype... more The locus of the foot of the perpendicular from a point O to a tangent hyperplane of a given hypersurface M in Euclidean space E n+1 is called the pedal of M with respect to O. Applications of the pedal in differential geometry can be found in papers by Th. Hasanis and D. Koutroufiotis [J. Geom. 24, 131-167 (1985; Zbl 0578.53002)], Chr. Georgiou, Th. Hasanis and D. Koutroufiotis [Geom. Dedicata 28, 153-169 (1988; Zbl 0659.53004)]. In the paper under review, the authors try to study the differential geometry of the pedal of a hypersurface with a constant support function. The study is trivial since in that case the pedal is a hypersphere. Euclidean hypersurfaces with a constant support function have been classified by Th. Hasanis and D. Koutroufiotis [Arch. Math. 57, 189-192 (1991; Zbl 0697.53012)].

Research paper thumbnail of Biharmonic Hypersurfaces of Lorentzian Para-Sasakian Manifolds

Research paper thumbnail of On A Semi-Symmetric On Non-Metric Connection In An Lp-Sasakian Manifold

International electronic journal of geometry, Oct 30, 2010

Research paper thumbnail of On a Semi-Symmetric Non-Metric Connection in an LP-Sasakian Manifold

Research paper thumbnail of Einstein like (epsilon)-para Sasakian manifolds

Research paper thumbnail of Curves Assocıated with an M Vector Field on a Semi Riemannian Hypersurface M of a Lorentzian Manifold M

Research paper thumbnail of The Stability Problem of Certain Anti-Invariant Submanifolds in Golden Riemannian Manifolds

International electronic journal of geometry, Apr 30, 2023

In this study, we discuss the stability of some anti-invariant submanifolds of golden Riemannian ... more In this study, we discuss the stability of some anti-invariant submanifolds of golden Riemannian manifolds under certain conditions in terms of the Ricci curvature tensors of the ambient manifold and the submanifold.

Research paper thumbnail of Einstein Metrics Induced by Natural Riemann Extensions

Advances in Applied Clifford Algebras, Mar 21, 2017

Clifford algebras are used in theoretical physics and in particular, in the general theory of rel... more Clifford algebras are used in theoretical physics and in particular, in the general theory of relativity, where Einstein's equations are rewritten in Girard (Adv Appl Clifford Algebras 9(2):225-230, 1999) within a Clifford algebra. Let M be a manifold with a torsion-free connection which induces on its cotangent bundle T * M , a semi-Riemannian metricḡ, called the natural Riemann extension, Kowalski and Sekizawa (Publ Math Debrecen 78:709-721, 2011). The main result of the present paper gives a necessary and sufficient condition forḡ restricted to certain hypersurfaces of T * M to be Einstein.

Research paper thumbnail of On Invariant Submanifolds of Riemannian Warped Product Manifold

Turkish Journal of Mathematics, Mar 1, 2003

In this paper, we generalize the geometry of the invariant submanifolds of Riemannian product man... more In this paper, we generalize the geometry of the invariant submanifolds of Riemannian product manifold to the geometry of the invariant submanifolds of Riemannian warped product manifold. We investigate some properties of an invariant submanifolds of a Riemannian warped product manifold. We show that every invariant submanifold of the Riemannian warped product manifold is a Riemannian warped product manifold. Also, we give a theorem on the pseudo-umbilical invariant submanifold. Further, we obtain that integral manifolds on an invariant submanifold are curvature-invariant submanifolds. Finally, we give a necessary condititon on a totally umbilical invariant submanifold to be totally geodesic.

Research paper thumbnail of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:msub><mml:mrow><mml:mo st...

Journal of Geometry and Physics, Nov 1, 2021

Abstract In this paper, we define and study two new structures on a differentiable manifold calle... more Abstract In this paper, we define and study two new structures on a differentiable manifold called by us an f ( a , b ) ( 3 , 2 , 1 ) -structure and a framed f ( a , b ) ( 3 , 2 , 1 ) -structure as a generalization of some geometric structures determined by polynomial structures, where a , b ∈ R and b ≠ 0 . At beginning, we present some examples regarding f ( a , b ) ( 3 , 2 , 1 ) -structures and establish their some fundamental properties. We also give a necessary condition for an f ( a , b ) ( 3 , 2 , 1 ) -structure to be an almost quadratic ϕ-structure. Later, it is shown that the existence of two semi-Riemannian metrics on differentiable manifolds admitting a framed f ( a , b ) ( 3 , 2 , 1 ) -structure, i.e., framed f ( a , b ) ( 3 , 2 , 1 ) -manifolds. In particular, a framed f ( a , b ) ( 3 , 2 , 1 ) -manifold endowed with the first semi-Riemannian metric mentioned above is called a framed metric f ( a , b ) ( 3 , 2 , 1 ) -manifold. Finally, we construct some examples to illustrate the existence of framed metric f ( a , b ) ( 3 , 2 , 1 ) -manifolds.

Research paper thumbnail of On Lightlike Hypersurfaces of a Semi-Riemannian Space form

DergiPark (Istanbul University), Feb 1, 2003

In this paper, we study a Lightlike hypersurface of a semi-Riemann manifold. We show that a light... more In this paper, we study a Lightlike hypersurface of a semi-Riemann manifold. We show that a lightlike hypersurface is totally geodesic if and only if it is locally symmetric. Also, we show that a lightlike Hypersurface of IR 4m 4q (m, q > 1) is totally geodesic under some restrictions. Finally, we give some results on Ricci curvature of a lightlike hypersurface to be symmetric.

Research paper thumbnail of Chen invariants for Riemannian submersions and their applications in meteorology

arXiv (Cornell University), Feb 17, 2017

In this paper, an optimal inequality involving the delta curvature is exposed. An application of ... more In this paper, an optimal inequality involving the delta curvature is exposed. An application of Riemannian submersions dealing meteorology is presented. Some characterizations about the vertical motion and the horizontal divergence are obtained.

Research paper thumbnail of Ricci Soliton Lightlike Submanifolds with Co-Dimension <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2</span></span></span></span>

Fundamental journal of mathematics and applications, Jun 30, 2023

The necessary requirements for half-lightlike and coisotropic lightlike submanifolds to be a Ricc... more The necessary requirements for half-lightlike and coisotropic lightlike submanifolds to be a Ricci soliton are obtained. Some examples of Ricci soliton half-lightlike and Ricci soliton coisotropic lightlike submanifolds are given. The Ricci soliton equation is investigated on totally geodesic, totally umbilical, and irrotational lightlike submanifolds.

Research paper thumbnail of Legendre Curves on Generalized Paracontact Metric Manifolds

Bulletin of the Malaysian Mathematical Sciences Society, Mar 1, 2017

Two different notions of almost paracontact structures (which are compatible or anti-compatible w... more Two different notions of almost paracontact structures (which are compatible or anti-compatible with the metric), well known in the literature, are unified and generalized here. Several formulas of paraholomorphic maps are established, and a result of Lichnerowicz type is obtained. The connection transformations which have the same system of paracontact-planar Legendre curves are characterized. Conformal changes of metrics which preserve geodesics (resp. paracontact-planar Legendre curves) are studied.

Research paper thumbnail of Totally umbilical semi-invariant submanifolds in locally decomposable metallic Riemannian manifolds

Filomat

In this paper, we obtain some classification theorems for totally umbilical semi-invariant subman... more In this paper, we obtain some classification theorems for totally umbilical semi-invariant submanifolds in locally decomposable metallic Riemannian manifolds. We also prove that there exist no totally umbilical proper semi-invariant submanifolds in a posivitely or negatively curved locally decomposable metallic Riemannian manifold

Research paper thumbnail of Some characterizations on indefinite space forms admitting almost contact structures

Asian-European Journal of Mathematics

In this paper, the projective curvature tensor field of a generalized indefinite Sasakian space f... more In this paper, the projective curvature tensor field of a generalized indefinite Sasakian space form is investigated. Some results dealing with projectively semi-symmetric and [Formula: see text]-projectively semi-symmetric generalized indefinite Sasakian space forms are obtained. Furthermore, biharmonic Legendre Frenet curves are discussed on these manifolds.

Research paper thumbnail of Hypersurfaces of LP-Sasakian manifolds

arXiv: Differential Geometry, 2009

In this paper, we study the invariant and non-invariant hypersurfaces of (1,1)(1,1)(1,1) almost contact m... more In this paper, we study the invariant and non-invariant hypersurfaces of (1,1)(1,1)(1,1) almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively.

Research paper thumbnail of Inequalities for scalar curvature of pseudo-Riemannian submanifolds

Journal of Geometry and Physics, 2017

Abstract Some basic inequalities, involving the scalar curvature and the mean curvature, for a ps... more Abstract Some basic inequalities, involving the scalar curvature and the mean curvature, for a pseudo-Riemannian submanifold of a pseudo-Riemannian manifold are obtained. We also find inequalities for spacelike submanifolds. Equality cases are also discussed.