scholarly journals On ϕ-Recurrent Para-Sasakian Manifold Admitting Quarter-Symmetric Metric Connection

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
K. T. Pradeep Kumar ◽  
Venkatesha ◽  
C. S. Bagewadi
Keyword(s):  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Riemannian Connection ◽  
Metric Connection

We obtained the relation between the Riemannian connection and the quarter-symmetric metric connection on a para-Sasakian manifold. Further, we study ϕ-recurrent and concircular ϕ-recurrent para-Sasakian manifolds with respect to quarter-symmetric metric connection.

scholarly journals On δ- Lorentzian trans Sasakian manifold with semi-symmetric metric connection

2021 ◽  
Vol 39 (5) ◽  
pp. 113-135
Author(s):  
Mohd Danish Siddiqi
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Sasakian Manifold ◽  
Conformally Flat ◽  
Sasakian Manifolds ◽  
Projectively Flat ◽  
Metric Connection ◽  
Flat Manifolds ◽  
Curvature Tensors

The aim of the present research is to study the δ-Lorentzian trans Sasakian manifolds with a semi-symmetric metric connection. We have found the expressions for curvature tensors, Ricci curvature tensors and scalar curvature of the δ-Lorentzian trans Sasakian manifolds with a semi-symmetric metric and metric connection. Also, we have discussed some results on quasi-projectively flat and ϕ-projectively flat manifolds endowed with a semi-symmetric-metric connection. It shown that the manifold satisfying¯R. ¯ S = 0,¯P, ¯ S = 0.Lastly, we have obtained the conditions for the δ-Lorentzian Trans Sasakian manifolds with a semi-symmetric metric connection to be conformally flat and ξ-conformally flat.

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 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 Lightlike hypersurfaces of an (ε)-para Sasakian manifold with a semi-symmetric non-metric connection

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5767-5786
Author(s):  
Feyza Erdoğan ◽  
Selcen Perktaş
Keyword(s):  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Totally Geodesic ◽  
Lightlike Hypersurface ◽  
Ambient Manifold ◽  
Integrability Conditions ◽  
Metric Connection ◽  
Lightlike Hypersurfaces

In the present paper, we study a lightlike hypersurface, when the ambient manifold is an (?)-para Sasakian manifold endowed with a semi-symmetric non-metric connection. We obtain a condition for such a lightlike hypersurface to be totally geodesic. We define invariant and screen semi-invariant lightlike hypersurfaces of (?)-para Sasakian manifolds with a semi-symmetric non-metric connection. Also, we obtain integrability conditions for the distributions D ? ??? and D' ? ??? of a screen semi-invariant lightlike hypersurface of an (?)-para Sasakian manifolds with a semi-symmetric non-metric connection.

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 Some classes of 3-dimensional Trans-Sasakian manifolds with respect to semi-symmetric metric connection

2022 ◽  
Vol 40 ◽  
pp. 1-12
Author(s):  
Sampa Pahan
Keyword(s):  
Vector Field ◽  
Sasakian Manifold ◽  
Necessary Condition ◽  
Sasakian Manifolds ◽  
3 Dimensional ◽  
Metric Connection

The object of the present paper is to study semi-symmetric metric connection on a 3-dimensional trans-Sasakian manifold. We found the necessary condition under which a vector field on a 3-dimensional trans-Sasakian manifold will be a strict contact vector field. Then, we obtained extended generalized phi-recurrent 3-dimensional trans-Sasakian manifold with respect to semi-symmetric metric connection. Next, a 3-dimensional trans-Sasakian manifold satises the condition ~L.~ S = 0 with respect to semi-symmetric metric connection is studied.

scholarly journals Characterizations of the Total Space (Indefinite Trans-Sasakian Manifolds) Admitting a Semi-Symmetric Metric Connection

Axioms ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 68
Author(s):  
Dae Jin ◽  
Jae Lee
Keyword(s):  
Space Form ◽  
Sasakian Manifold ◽  
Total Space ◽  
Sasakian Space Form ◽  
Sasakian Manifolds ◽  
Metric Connection ◽  
Generalized Sasakian Space Form ◽  
Lightlike Hypersurfaces ◽  
Kenmotsu Space Form

We investigate recurrent, Lie-recurrent, and Hopf lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a semi-symmetric metric connection. In these hypersurfaces, we obtain several new results. Moreover, we characterize that the total space (an indefinite generalized Sasakian space form) with a semi-symmetric metric connection is an indefinite Kenmotsu space form under various lightlike hypersurfaces.

scholarly journals Different Types of Curvature and Their Vanishing Conditions

2021 ◽  
pp. 143-148
Author(s):  
Manisha Maheshkumar Kankarej
Keyword(s):  
Comparative Study ◽  
Sasakian Manifold ◽  
Riemannian Curvature ◽  
Weyl Curvature ◽  
Projective Curvature ◽  
Hessian Operator ◽  
Different Types ◽  
Riemannian Connection ◽  
Metric Connection

In the present paper, I studied different types of Curvature like Riemannian Curvature, Concircular Curvature, Weyl Curvature, and Projective Curvature in Quarter Symmetric non-Metric Connection in P-Sasakian manifold. A comparative study of a manifold with a Riemannian connection is done with a P-Sasakian Manifold. Conditions for vanishing for different types of curvature are also a part of the study. Some necessary properties of the Hessian operator are discussed with respect to all curvatures as well.

scholarly journals A note on quasi-generalized CR-lightlike geometry in indefinite nearly μ-Sasakian manifolds

2017 ◽  
Vol 14 (03) ◽  
pp. 1750045
Author(s):  
Fortuné Massamba ◽  
Samuel Ssekajja
Keyword(s):  
Existence Theorem ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Metric Connection ◽  
Nearly Sasakian ◽  
Main Ideas ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

The concept of quasi-generalized CR-lightlike was first introduced by the authors in [Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds, Arab. J. Math. 5 (2016) 87–101]. In this paper, we focus on ascreen and co-screen quasi-generalized CR-lightlike submanifolds of indefinite nearly [Formula: see text]-Sasakian manifold. We prove an existence theorem for minimal ascreen quasi-generalized CR-lightlike submanifolds admitting a metric connection. Classification theorems on nearly parallel and auto-parallel distributions on a co-screen quasi-generalized CR-lightlike submanifold are also given. Several examples are also constructed, where necessary, to illustrate the main ideas.

Some Properties of Para-Sasakian Manifolds

2017 ◽  
Vol 5 (2) ◽  
pp. 73-78
Author(s):  
Jay Prakash Singh ◽  
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Sasakian Manifold ◽  
Subject Classification ◽  
Killing Vector Field ◽  
Sasakian Manifolds ◽  
Geometric Properties ◽  
Paper Author

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.

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