scholarly journals The curvature tensor of $$(\kappa ,\mu ,\nu )$$ ( κ , μ , ν ) -contact metric manifolds

2015 ◽  
Vol 177 (3) ◽  
pp. 331-344
Author(s):  
Kadri Arslan ◽  
Alfonso Carriazo ◽  
Verónica Martín-Molina ◽  
Cengizhan Murathan
Keyword(s):  
Curvature Tensor ◽  
Contact Metric Manifolds

scholarly journals Conharmonic Curvature Tensor on -Contact Metric Manifolds

ISRN Geometry ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Sujit Ghosh ◽  
U. C. De ◽  
A. Taleshian
Keyword(s):  
Curvature Tensor ◽  
Contact Metric Manifolds ◽  
Conharmonic Curvature Tensor ◽  
Flat Contact

The object of the present paper is to characterize -contact metric manifolds satisfying certain curvature conditions on the conharmonic curvature tensor. In this paper we study conharmonically symmetric, -conharmonically flat, and -conharmonically flat -contact metric manifolds.

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 A Study on ϕ-recurrence τ-curvature tensor in (k, µ)-contact metric manifolds

2018 ◽  
Vol 26 (2) ◽  
pp. 1-10
Author(s):  
Gurupadavva Ingalahalli ◽  
C.S. Bagewadi
Keyword(s):  
Curvature Tensor ◽  
Contact Metric Manifolds

AbstractIn this paper we study ϕ-recurrence τ -curvature tensor in (k, µ)-contact metric manifolds.

scholarly journals Classification of Ricci semisymmetric contact metric manifolds

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2527-2535
Author(s):  
Pradip Majhi ◽  
Uday De
Keyword(s):  
Curvature Tensor ◽  
Second Order ◽  
Curvature Condition ◽  
Ricci Operator ◽  
Contact Metric Manifolds ◽  
Order Parallel ◽  
Symmetric Properties

The object of the present paper is to study Ricci semisymmetric contact metric manifolds. As a consequence of the main result we deduce some important corollaries. Besides these we study contact metric manifolds satisfying the curvature condition Q,R = 0, where Q and R denote the Ricci operator and curvature tensor respectively. Also we study the symmetric properties of a second order parallel tensor in contact metric manifolds. Finally, we give an example to verify the main result.

scholarly journals E-BOCHNER CURVATURE TENSOR ON ( κ , µ)-CONTACT METRIC MANIFOLDS

2014 ◽  
Vol 7 (1) ◽  
pp. 143-153 ◽  
Author(s):  
Uday CHAND DE ◽  
Srimayee SAMUI
Keyword(s):  
Curvature Tensor ◽  
Contact Metric Manifolds

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

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1383-1392
Author(s):  
İnan Ünal ◽  
Mustafa Altın
Keyword(s):  
Curvature Tensor ◽  
Space Form ◽  
Sasakian Space Form ◽  
Contact Metric Manifold ◽  
Contact Metric Manifolds ◽  
Generalized Sasakian Space Form ◽  
Concircular Curvature Tensor

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.

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