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.

Certain Properties of τ -Curvature Tensor in Generalized Sasakian Space Form

2020 ◽  
Vol 8 (2) ◽  
pp. 83-94
Author(s):  
C. Lalmalsawma ◽  
◽  
J.P. Singh ◽  
Keyword(s):  
Curvature Tensor ◽  
Space Form ◽  
Sasakian Space Form ◽  
Generalized Sasakian Space Form

In this paper we study τ-curvature tensor in generalized Sasakian-space-form. We study semisymmetric generalized Sasakian-space-form and obtain results for particular cases. We also study generalized Sasakian-space-form satisfying . We also obtain some results for all particular cases of τ -Curvature tensor.

scholarly journals Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Dae Ho Jin
Keyword(s):  
Vector Field ◽  
Space Form ◽  
Sasakian Manifold ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Structure ◽  
Sasakian Space Forms ◽  
Generalized Sasakian Space Form ◽  
Characterization Theorems ◽  
Lightlike Hypersurfaces

We study lightlike hypersurfacesMof an indefinite generalized Sasakian space formM-(f1,f2,f3), with indefinite trans-Sasakian structure of type(α,β), subject to the condition that the structure vector field ofM-is tangent toM. First we study the general theory for lightlike hypersurfaces of indefinite trans-Sasakian manifold of type(α,β). Next we prove several characterization theorems for lightlike hypersurfaces of an indefinite generalized Sasakian space form.

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 Some Curvature Properties on Lorentzian Generalized Sasakian-Space-Forms

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Rongsheng Ma ◽  
Donghe Pei
Keyword(s):  
Space Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Conformally Flat ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Projectively Flat ◽  
Generalized Sasakian Space Form ◽  
Necessary And Sufficient

In this paper, we investigate the Lorentzian generalized Sasakian-space-form. We give the necessary and sufficient conditions for the Lorentzian generalized Sasakian-space-form to be projectively flat, conformally flat, conharmonically flat, and Ricci semisymmetric and their relationship between each other. As the application of our theorems, we study the Ricci almost soliton on conformally flat Lorentzian generalized Sasakian-space-form.

Symmetries of Sasakian Generalized Sasakian-Space-Form Admitting Generalized Tanaka–Webster Connection

2021 ◽  
Vol 52 ◽  
Author(s):  
Chawngthu Lalmalsawma ◽  
Jay Prakash Singh
Keyword(s):  
Space Form ◽  
Sasakian Space Form ◽  
Generalized Sasakian Space Form ◽  
Symmetric Properties

The object of this paper is to study symmetric properties of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. We studied semisymmetry and Ricci semisymmetry of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. Further we obtain results for Ricci pseudosymmetric and Ricci-generalized pseudosymmetric Sasakian generalized Sasakian-space-form.

scholarly journals Chen-Ricci Inequalities with a Quarter Symmetric Connection in Generalized Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ali H. Al-Khaldi ◽  
Mohd. Aquib ◽  
Mohd Aslam ◽  
Meraj Ali Khan
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Lagrangian Submanifold ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Generalized Complex ◽  
Metric Connection ◽  
Generalized Sasakian Space Form ◽  
Symmetric Connection ◽  
Legendrian Submanifold

In this article, we obtain improved Chen-Ricci inequalities for submanifolds of generalized space forms with quarter-symmetric metric connection, with the help of which we completely characterized the Lagrangian submanifold in generalized complex space form and a Legendrian submanifold in a generalized Sasakian space form. We also discuss some geometric applications of the obtained results.

scholarly journals Ricci soliton and η-Ricci soliton on Generalized Sasakian space form

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4051-4062 ◽  
Author(s):  
Sampa Pahan ◽  
Tamalika Dutta ◽  
Arindam Bhattacharyya
Keyword(s):  
Space Form ◽  
Ricci Soliton ◽  
Sasakian Space Form ◽  
Generalized Sasakian Space Form
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