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 Lightlike Geometry of Para-Sasakian Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Bilal Eftal Acet ◽  
Selcen Yüksel Perktaş ◽  
Erol Kılıç
Keyword(s):  
Vector Field ◽  
Characteristic Vector ◽  
Sasakian Manifolds ◽  
Lightlike Hypersurface ◽  
Sasakian Structure ◽  
Integrability Conditions ◽  
Integrable Distribution ◽  
Lightlike Hypersurfaces ◽  
Characteristic Vector Field

We study lightlike hypersurfaces of para-Sasakian manifolds tangent to the characteristic vector field. In particular, we define invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, respectively, and give examples. Integrability conditions for the distributions on a screen semi-invariant lightlike hypersurface of para-Sasakian manifolds are investigated. We obtain a para-Sasakian structure on the leaves of an integrable distribution of a screen semi-invariant lightlike hypersurface.

scholarly journals Radical transversal SCR-lightlike submanifolds of indefinite Sasakian manifolds

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2585-2594
Author(s):  
S.S. Shukla ◽  
Akhilesh Yadav
Keyword(s):  
Sufficient Conditions ◽  
Characterization Theorem ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Manifolds ◽  
Totally Geodesic ◽  
Integrability Conditions ◽  
Cauchy Riemann ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds

In this paper, we introduce the notion of radical transversal screen Cauchy-Riemann (SCR)- lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some nontrivial examples of such submanifolds. Integrability conditions of distributions D1, D2, D and D? on radical transversal SCR-lightlike submanifolds of an indefinite Sasakian manifold have been obtained. Further, we obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic.

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 Lightlike submanifolds of metallic semi-Riemannian manifolds

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1781-1794
Author(s):  
Perktaş Yüksel ◽  
Feyza Erdoğan ◽  
Bilal Acet
Keyword(s):  
Riemannian Manifolds ◽  
Integrability Conditions ◽  
Metric Connection ◽  
Lightlike Submanifolds ◽  
Lightlike Hypersurfaces

Our aim in this paper is to investigate some special types of lightlike submanifolds in metallic semi-Riemannian manifolds. We study invariant lightlike submanifolds and screen semi-invariant lightlike hypersurfaces of metallic semi-Riemannian manifolds and give examples. We obtain some conditions for the induced connection to be a metric connection and present integrability conditions for the distributions involved in the definitions of such types.

scholarly journals Contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold

2013 ◽  
Vol 5 (2) ◽  
pp. 157-168
Author(s):  
Barnali Laha ◽  
Bandana Das ◽  
Arindam Bhattacharyya
Keyword(s):  
Sasakian Manifold ◽  
Invariant Distribution ◽  
Sasakian Manifolds ◽  
Totally Geodesic ◽  
Cr Submanifolds

Abstract In this paper we prove some properties of the indefinite Lorentzian para-Sasakian manifolds. Section 1 is introductory. In Section 2 we define D-totally geodesic and D⊥-totally geodesic contact CRsubmanifolds of an indefinite Lorentzian para-Sasakian manifold and deduce some results concerning such a manifold. In Section 3 we state and prove some results on mixed totally geodesic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold. Finally, in Section 4 we obtain a result on the anti-invariant distribution of totally umbilic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold.

scholarly journals Noninvariant Hypersurfaces of a Nearly Trans-Sasakian Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Satya Prakash Yadav ◽  
Shyam Kishor
Keyword(s):  
Contact Structure ◽  
Sasakian Manifold ◽  
Necessary Condition ◽  
Sasakian Manifolds ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Cosymplectic Manifold ◽  
Cosymplectic Manifolds ◽  
Nearly Cosymplectic

The present paper focuses on the study of noninvariant hypersurfaces of a nearly trans-Sasakian manifold equipped with(f,g,u,v,λ)-structure. Initially some properties of this structure have been discussed. Further, the second fundamental forms of noninvariant hypersurfaces of nearly trans-Sasakian manifolds and nearly cosymplectic manifolds with(f,g,u,v,λ)-structure have been calculated providedfis parallel. In addition, the eigenvalues offhave been found and proved that a noninvariant hypersurface with(f,g,u,v,λ)-structure of nearly cosymplectic manifold with contact structure becomes totally geodesic. Finally the paper has been concluded by investigating the necessary condition for totally geodesic or totally umbilical noninvariant hypersurface with(f,g,u,v,λ)-structure of a nearly trans-Sasakian manifold.

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 On contact CR-submanifolds of sasakian manifolds

1983 ◽  
Vol 6 (2) ◽  
pp. 313-326
Author(s):  
Koji Matsumoto
Keyword(s):  
Space Form ◽  
Sasakian Manifold ◽  
Second Fundamental Form ◽  
Sasakian Space Form ◽  
Sasakian Manifolds ◽  
Fundamental Properties ◽  
The Second Fundamental Form ◽  
Ambient Manifold ◽  
The One ◽  
Kaehlerian Manifold

Recently, K.Yano and M.Kon [5] have introduced the notion of a contactCR-submanifold of a Sasakian manifold which is closely similar to the one of aCR-submanifold of a Kaehlerian manifold defined by A. Bejancu [1].In this paper, we shall obtain some fundamental properties of contactCR-submanifolds of a Sasakian manifold. Next, we shall calculate the length of the second fundamental form of a contactCR-product of a Sasakian space form (THEOREM 7.4). At last, we shall prove that a totally umbilical contactCR-submanifold satisfying certain conditions is totally geodesic in the ambient manifold (THEOREM 8.1).

Sign in / Sign up

Export Citation Format

Share Document