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

2019 ◽  
Vol 22 (2) ◽  
pp. 279-292
Author(s):  
Abdul Haseeb ◽  
Rajendra Prasad
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Metric Connection ◽  
Concircular Curvature Tensor

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.

scholarly journals Quarter-Symmetric Nonmetric Connection on P-Sasakian Manifolds

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Abul Kalam Mondal ◽  
U. C. De
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Second Order ◽  
Sasakian Manifolds ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Metric Connection ◽  
Concircular Curvature Tensor ◽  
Order Parallel

The object of the present paper is to study a quarter-symmetric nonmetric connection on a P-Sasakian manifold. In this paper we consider the concircular curvature tensor and conformal curvature tensor on a P-Sasakian manifold with respect to the quarter-symmetric nonmetric connection. Next we consider second-order parallel tensor with respect to the quarter-symmetric non-metric connection. Finally we consider submanifolds of an almost paracontact manifold with respect to a quarter-symmetric non-metric connection.

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

2021 ◽  
Vol 110 (124) ◽  
pp. 91-102
Author(s):  
Ajit Barman
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Metric Connection ◽  
Concircular Curvature Tensor

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

scholarly journals Quarter-symmetric metric connection in a P-Sasakian manifold

2015 ◽  
Vol 53 (1) ◽  
pp. 137-150 ◽  
Author(s):  
Krishanu Mandal ◽  
Uday Chand De
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Metric Connection

Abstract In this paper, we consider a quarter-symmetric metric connection in a P-Sasakian manifold. We investigate the curvature tensor and the Ricci tensor of a P-Sasakian manifold with respect to the quarter-symmetric metric connection. We consider semisymmetric P-Sasakian manifold with respect to the quarter- symmetric metric connection. Furthermore, we consider generalized recurrent P-Sasakian manifolds and prove the non-existence of recurrent and pseudosymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Finally, we construct an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection which verifies Theorem 4.1.

scholarly journals Concircular Curvature Tensor of a Semi-symmetric Non-metric Connection on P-Sasakian Manifolds

2016 ◽  
Vol 54 (2) ◽  
pp. 47-58 ◽  
Author(s):  
Ajit Barman ◽  
Gopal Ghosh
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifolds ◽  
Metric Connection ◽  
Concircular Curvature Tensor

Abstract The object of the present paper is to study P-Sasakian manifolds admitting a semi-symmetric non-metric connection whose concircular curvature tensor satisfies certain curvature conditions

scholarly journals On Para-Sasakian manifolds admitting semi-symmetric metric connection

2014 ◽  
Vol 95 (109) ◽  
pp. 239-247 ◽  
Author(s):  
Ajit Barman
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Projective Curvature ◽  
Metric Connection ◽  
Projective Curvature Tensor

We study a Para-Sasakian manifold admitting a semi-symmetric metric connection whose projective curvature tensor satisfies certain curvature conditions.

scholarly journals On some classes of invariant submanifolds of lorentzian para-sasakian manifolds

2016 ◽  
Vol 47 (2) ◽  
pp. 207-220
Author(s):  
Srimayee Samui ◽  
Uday Chand De
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Invariant Submanifolds ◽  
Concircular Curvature Tensor

The object of the present paper is to study invariant submanifolds of Lorenzian Para-Sasakian manifolds. We consider the recurrent and bi-recurrent invariant submanifolds of Lorentzian para-Sasakian manifolds and pseudo-parallel and generalized Ricci pseudo-parallel invariant submanifolds of Lorentzian para-Sasakian manifolds. Also we search for the conditions $\mathcal{Z}(X,Y)\cdot\alpha=fQ(g,\alpha)$ and $\mathcal{Z}(X,Y)\cdot\alpha=fQ(S,\alpha)$ on invariant submanifolds of Lorentzian para-Sasakian manifolds, where $\mathcal{Z}$ is the concircular curvature tensor. Finally, we construct an example of an invariant submanifold of Lorentzian para Sasakian manifold.

scholarly journals Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Bilal Eftal Acet ◽  
Erol Kılıç ◽  
Selcen Yüksel Perktaş
Keyword(s):  
Curvature Tensor ◽  
Einstein Manifold ◽  
Constant Scalar Curvature ◽  
Sasakian Manifold ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Concircular Curvature Tensor

We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is anη-Einstein manifold. We also investigate some properties of curvature tensor, conformal curvature tensor,W2-curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor with respect to canonical paracontact connection on a para-Sasakian manifold. It is shown that a concircularly flat para-Sasakian manifold with respect to canonical paracontact connection is of constant scalar curvature. We give some characterizations for pseudo-projectively flat para-Sasakian manifolds.

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