Concircular Curvature Tensor Research Articles

Curvature properties of metric and semi-symmetric linear connections

Considering a non-symmetric linear connection and its dual one appear 6 independent curvature tensors [15]. In the present paper we study properties of curvature tensors of semi-symmetric metric connections on a generalized Riemannian manifold. It is shown that if linear connection preserves the symmetric part of the generalized Riemannian metric with semi-symmetric torsion with an appropriate additional condition, then these six curvature tensors can be expressed by linear combination of Weyl conformal curvature tensor, Weyl projective curvature tensor and the concircular curvature tensor. In the case of the curvature tensor , we have proved that if exists a linear connection preserving the symmetric part of the generalized Riemannian metric with semi-symmetric torsion, whose curvature tensor vanishes, it is necessary and sufficient that the Riemannian metric be projectively flat. For tensor we also get a useful result. If exists a linear connection preserving the symmetric part of the generalized Riemannian metric with semi-symmetric torsion, whose curvature tensor and Ricci tensor vanish, it is necessary and sufficient that the Riemannian metric be conformally flat.

On $f$-Kenmotsu manifolds admitting Schouten-Van Kampen connection

In the present paper, we study three-dimensional $f$-Kenmotsu manifolds admitting the Schouten-Van Kampen connection. We study the concircular curvature tensor of a three-dimensional $f$-Kenmotsu manifold with respect to the Schouten-Van Kampen connection. Finally, we have cited an example of a three-dimensional $f$-Kenmotsu manifold admitting Schouten-Van Kampen connection which verify our results.

On Metric Contact Pairs with Certain Semi-Symmetry Conditions

Blair et al. [7] introduced the notion of bicontact manifold in the context of Hermitian geometry. Bande and Hadjar [1] studied on this notion under the name of contact pairs. These type of structures have important properties and their geometry is some different from classical contact structures. In this paper, we study on some semi-symmetry properties of the normal contact pair manifolds. We prove that a Ricci semi-symmetric (or concircularly Ricci semi-symmetric) normal metric contact pair manifold is a generalized quasi-Einstein manifold. Also, we classify normal metric contact pair manifolds as a generalized quasi-Einstein manifold with certain semi-symmetry conditions and for the concircular curvature tensor , the Riemannian curvature tensor , and an arbitrary vector field .

A note on concircular curvature tensor in Lorentzian almost para-contact geometry

The paper deals with the notion of different classes of concircular curvature tensor on Lorentzian almost para-contact manifolds admitting a quarter-symmetric metric connection. In this paper we study Lorentzian almost para-contact manifolds with respect to the quarter-symmetric metric connection satisfying the curvature condition Z.S = 0. We also investigate the properties of ξ−concircularly flat, φ−concircularly flat and quasi-concircularly flat Lorentzian almost para-contact manifolds admitting a quarter-symmetric metric connection and it is found that in each of above cases the manifold is generalized η−Einstein manifold.

On a type of quarter-symmetric non-recurrent metric connection on a p-Sasakian manifold

We study a Para-Sasakian manifold admitting a type of quartersymmetric non-recurrent-metric connection whose concircular curvature tensor satisfies certain curvature conditions.

N(k)-contact metric manifolds with generalized Tanaka-Webster connection

In this paper, we characterize N(k)-contact metric manifolds with generalized Tanaka-Webster connection. We obtain some curvature properties. It is proven that if an N(k)-contact metric manifold with generalized Tanaka-Webster connection is K-contact then it is an example of generalized Sasakian space form. Also, we examine some flatness and symmetric conditions of concircular curvature tensor on an N(k)-contact metric manifolds with generalized Tanaka-Webster connection.

Generalized Quasi-Einstein Manifolds in Contact Geometry

In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It is proved that a normal metric contact pair manifold with generalized quasi-constant curvature is a generalized quasi-Einstein manifold. Normal metric contact pair manifolds satisfying cyclic parallel Ricci tensor and the Codazzi type of Ricci tensor are considered, and further prove that a generalized quasi-Einstein normal metric contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally, we characterize normal metric contact pair manifolds satisfying certain curvature conditions related to M-projective, conformal, and concircular curvature tensors. We show that a normal metric contact pair manifold with generalized quasi-constant curvature is locally isometric to the Hopf manifold S2n+1(1)×S1.

Geometry of concircular curvature tensor of Kahler manifolds

The study deals with the necessary condition where a nearly Kahler manifold of flat concircular tensor has been found. And the relationship between these invariants and additional properties of symmetry concircular tensor, as well as geometrical meaning of the reference in zero of these invariants .

Some curvature proprieties of Kenmotsu manifolds with the Schouten-van Kampen connection

The aim of the present paper is to study the concircular curvature tensor, projective curvature tensor, Weyl conformal curvature tensor of Kenmotsu manifolds admitting Schouten-van Kampen connection and an example is given to verify our results.

Concircular Curvature on Warped Product Manifolds and Applications

This study aims mainly at investigating the effects of concircular flatness and concircular symmetry of a warped product manifold on its fibre and base manifolds. Concircularly flat and concircularly symmetric warped product manifolds are investigated. The divergence free concircular curvature tensor on warped product manifolds is considered. Finally, we apply some of these results to generalized Robertson-Walker and standard static space-times.

Certain Curvature Conditions on P-Sasakian Manifolds Admitting a Quater-Symmetric Metric Connection

The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered. Next the authors study ξ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Furthermore, the authors study P-Sasakian manifolds satisfying the condition $$\tilde Z(\xi ,Y) \cdot \tilde S = 0$$, where $$\tilde Z, \tilde S$$ are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Finally, an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection is constructed.

Concircular curvature tensor of Kenmotsu manifolds admitting generalized Tanaka-Webster connection

The objective of the present paper is to study concircular curvature tensor of Kenmotsu manifold with respect to generalized Tanaka-Webster connection, whose concircular curvature tensor satisifies certain conditions and it is shown that if the curvature tensor of a Kenmotsu manifold admitting generalized Tanaka-Webster connection $\nabla^{*}$ vanishes, then the Kenmotsu manifold is locally isometric to the hyperbolic space $H^{2n+1}(-1)$. Further we have studied $\xi$-concircularly flat, $\phi$-concircularly flat, pseudo-concircularly flat, $C^{*} . \phi =0$, $C^{*}.S^{*}=0$ and we have shown that $R^{*} . C^{*}=R^{*} . R^{*}$. Finally, an example of a $5$-dimensional Kenmotsu manifold with respect to the generalized Tanaka-Webster connection is given to verify our result.

Genelleştirilmiş Kenmotsu Manifoldları Üzerinde Concircular Eğrilik Tensörü

The aim of the present paper is to study on concircular curvature tensor on generalized Kenmotsu manifolds. Concircular flat and -concircular flat generalized Kenmotsu manifolds are examined. Also some results are given about -semi symmetric and -concircular semi symmetric generalized Kenmotsu manifolds.

On concircular curvature tensor in a Lorentzian α-Sasakian manifold with respect to the quarter-symmetric non-metric connection

In the present paper, some properties of concircular curvature tensor in a Lorentzian α-Sasakian manifold with respect to the quarter-symmetric non-metric connection have been studied.

Concircular curvature tensor of Kenmotsu manifolds admitting generalized Tanaka-Webster connection

The objective of the present paper is to study concircular curvature tensor of Kenmotsu manifold with respect to generalized Tanaka-Webster connection, whose concircular curvature tensor satisifies certain conditions and it is shown that if the curvature tensor of a Kenmotsu manifold admitting generalized Tanaka-Webster connection $\nabla^{*}$ vanishes, then the Kenmotsu manifold is locally isometric to the hyperbolic space $H^{2n+1}(-1)$. Further we have studied $\xi$-concircularly flat, $\phi$-concircularly flat, pseudo-concircularly flat, $C^{*} . \phi =0$, $C^{*}.S^{*}=0$ and we have shown that $R^{*} . C^{*}=R^{*} . R^{*}$. Finally, an example of a $5$-dimensional Kenmotsu manifold with respect to the generalized Tanaka-Webster connection is given to verify our result.

On some classes of concircular curvature tensor on Lorentzian para-Sasakian manifolds

The present paper deals with the study of different classes of concircular curvature tensor on Lorentzian para-Sasakian manifold admitting a quarter-symmetric metric connection.

On Concircular Curvature Tensor in Space-Times

The aim of this work is to examine some properties of the concircular curvature tensor on $4-$dimensional manifolds admitting a Lorentz metric (so called space-times). In the first two sections, the study is introduced and the interrelated concepts together with some notations are presented. In the third section of the study, some results are obtained connected to eigenbivector structure of the concircular curvature tensor on these manifolds by taking into account the classification scheme of 2--forms (also known as bivectors) in this metric signature. Then, the known holonomy algebras on space-times are considered and some theorems are given regarding the concircular and Riemann curvature tensors. This analysis is also associated with the types of the Riemann curvature tensor on these manifolds. In the last section, the results of the study is summarized and the discussion part is presented.

P-Sasakian Manifold with Quarter-Symmetric Non-Metric Connection

The object of the present paper is to study on a P-Sasakian manifold with quarter symmetric non-metric connection. In this paper, we consider some properties of the curvature tensor, projective curvature tensor, concircular curvature tensor, conformal curvature tensor with respect to quarter symmetric non-metric connection in a P-Sasakian manifolds. Finally, we give an example.

Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold

In the present paper we have studied the curvature tensor of a normal paracontact metric manifold satisfying the conditions R(ξ,X)P=0, P(ξ,X)R=0, P(ξ,X)P=0, P(ξ,X)S=0, P(ξ,X)Z=0 and pseudo projective flatness, where R, P, S and Z denote the Riemannian curvature, pseudo projective curvature, Ricci and concircular curvature tensors, respectively.

Certain curvature conditions on Kenmotsu manifolds admitting a quarter-symmetric metric connection

We study certain curvature properties of Kenmotsu manifolds with respect to the quarter-symmetric metric connection. First we consider Ricci semisymmetric Kenmotsu manifolds with respect to a quarter-symmetric metric connection. Next, we study ξ-conformally flat and ξ-concircularly flat Kenmotsu manifolds with respect to the quarter-symmetric metric connection. Moreover, we study Kenmotsu manifolds satisfying the condition ˜Z(ξ,Y)• ˜S = 0, where ˜Z and ˜S are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Then, we prove the non-existence of ξ-projectively flat and pseudo-Ricci symmetric Kenmotsu manifolds with respect to the quarter-symmetric metric connection. Finally, we construct an example of a 5-dimensional Kenmotsu manifold admitting a quarter-symmetric metric connection for illustration.