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.

On M-Projective Curvature Tensor of Lorentzian α-Sasakian Manifolds

2017 ◽  
Vol 18 ◽  
pp. 22-31
Author(s):  
D.G. Prakasha ◽  
Vasant Chavan
Keyword(s):  
Curvature Tensor ◽  
Unit Sphere ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Projective Curvature Tensor

In this paper, we study the nature of Lorentzianα-Sasakian manifolds admitting M-projective curvature tensor. We show that M-projectively flat and irrotational M-projective curvature tensor of Lorentzian α-Sasakian manifolds are locally isometric to unit sphere Sn(c) , wherec = α2. Next we study Lorentzianα-Sasakian manifold with conservative M-projective curvature tensor. Finally, we find certain geometrical results if the Lorentzianα-Sasakian manifold satisfying the relation M(X,Y)⋅R=0.

scholarly journals ∗-Conformal η-Ricci soliton on Sasakian manifold

2021 ◽  
pp. 2250035
Author(s):  
Soumendu Roy ◽  
Santu Dey ◽  
Arindam Bhattacharyya ◽  
Shyamal Kumar Hui
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Ricci Soliton ◽  
Sasakian Manifolds ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Projective Curvature Tensor

In this paper, we study ∗-Conformal [Formula: see text]-Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting ∗-Conformal [Formula: see text]-Ricci soliton. We obtain some significant results on ∗-Conformal [Formula: see text]-Ricci soliton in Sasakian manifolds satisfying [Formula: see text], [Formula: see text], [Formula: see text] [Formula: see text], where [Formula: see text] is Pseudo-projective curvature tensor. The conditions for ∗-Conformal [Formula: see text]-Ricci soliton on [Formula: see text]-conharmonically flat and [Formula: see text]-projectively flat Sasakian manifolds have been obtained in this paper. Lastly we give an example of five-dimensional Sasakian manifolds satisfying ∗-Conformal [Formula: see text]-Ricci soliton.

scholarly journals Projective Curvature Tensor with Respect to Zamkovoy Connection in Lorentzian Para-Sasakian Manifolds

2020 ◽  
Vol 26 (3) ◽  
pp. 369-379
Author(s):  
Abhijit Mandal ◽  
Ashoke Das
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Curvature Tensors

The purpose of the present paper is to study some properties of the Projective curvature tensor with respect to Zamkovoy connection in Lorentzian Para Sasakian manifold(or,LP-Sasakian manifold)'And we have studied some results in Lorentzian Para-Sasakian manifold with the help of Zamkovoy connection and Projective curvature tensor.Also we discussed the LP-Sasakian manifold satisfying P*(ξ,U)∘W₀*=0,P*(ξ,U)∘W₂*=0 , where W₀*,W₂* and P* are W₀,W₂ and Projective curvature tensors with respect to Zamkovoy connection.

scholarly journals ON THE $\mathcal{M}$--PROJECTIVE CURVATURE TENSOR OF A $(k, \mu)$-CONTACT METRIC MANIFOLD

2017 ◽  
pp. 117
Author(s):  
D. G. Prakasha ◽  
Kakasab Mirji
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Sasakian Manifold ◽  
Riemannian Curvature ◽  
Contact Metric Manifold ◽  
Contact Metric Manifolds ◽  
Riemannian Curvature Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor

The paper deals with the study of $\mathcal{M}$-projective curvature tensor on $(k, \mu)$-contact metric manifolds. We classify non-Sasakian $(k, \mu)$-contact metric manifold satisfying the conditions $R(\xi, X)\cdot \mathcal{M} = 0$ and $\mathcal{M}(\xi, X)\cdot S =0$, where $R$ and $S$ are the Riemannian curvature tensor and the Ricci tensor, respectively. Finally, we prove that a $(k, \mu)$-contact metric manifold with vanishing extended $\mathcal{M}$-projective curvature tensor $\mathcal{M}^{e}$ is a Sasakian manifold.

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 On the Weyl projective curvature tensor of the projective semi-symmetric connection in an SP-Sasakian manifold

2020 ◽  
Vol 32 (9) ◽  
pp. 100-110
Author(s):  
TEERATHRAM RAGHUWANSHI ◽  
◽  
SHRAVAN KUMAR PANDEY ◽  
MANOJ KUMAR PANDEY ◽  
ANIL GOYAL ◽  
...  
Keyword(s):  
Curvature Tensor ◽  
Einstein Manifold ◽  
Sasakian Manifold ◽  
Projective Curvature ◽  
Symmetric Connection ◽  
Projective Curvature Tensor

The objective of the present paper is to study the W2-curvature tensor of the projective semi-symmetric connection in an SP-Sasakian manifold. It is shown that an SP-Sasakian manifold satisfying the conditions ܲ\simP ⋅W2\sim ܹ = 0 is an Einstein manifold and ܹW2\sim . ܲP\sim = 0 is a quasi Einstein manifold.

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.

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