scholarly journals Generalized Transversal Lightlike Submanifolds of Indefinite Sasakian Manifolds

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Classification Theorem ◽  
Sasakian Manifolds ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We introduce and study generalized transversal lightlike submanifold of indefinite Sasakian manifolds which includes radical and transversal lightlike submanifolds of indefinite Sasakian manifolds as its trivial subcases. A characteristic theorem and a classification theorem of generalized transversal lightlike submanifolds are obtained.

scholarly journals GCR-Lightlike Product of Indefinite Sasakian Manifolds

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Rakesh Kumar ◽  
Varun Jain ◽  
R. K. Nagaich
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We study mixed geodesicGCR-lightlike submanifolds of indefinite Sasakian manifolds and obtain some necessary and sufficient conditions for aGCR-lightlike submanifold to be aGCR-lightlike product.

scholarly journals On Totally Contact Umbilical Contact CR-Lightlike Submanifolds Of Indefinite Sasakian Manifolds

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
Manish Gogna ◽  
Rakesh Kumar ◽  
R. K. Nagaich
Keyword(s):  
Sasakian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

AbstractAfter brief introduction, we prove that a totally contact umbilical CR- lightlike submanifold is totally contact geodesic. We obtain a necessary and sufficient condition for a CR-lightlike submanifold to be an anti-invariant submanifold. Finally, we characterize a contact CR-lightlike submanifold of indefinite Sasakian manifold to be a contact CR-lightlike product

scholarly journals Slant lightlike submanifolds of indefinite Sasakian manifolds

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 277-287 ◽  
Author(s):  
Bayram Sahin ◽  
Cumali Yıldırım
Keyword(s):  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

In this paper, we define and study both slant lightlike submanifolds and screen slant lightlike submanifolds of an indefinite Sasakian manifold. We provide non-trivial examples and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold.

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 results on normal GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds

2019 ◽  
Vol 16 (03) ◽  
pp. 1950037
Author(s):  
Megha ◽  
Sangeet Kumar
Keyword(s):  
Sufficient Conditions ◽  
Characterization Theorem ◽  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Holomorphic Bisectional Curvature ◽  
Necessary And Sufficient ◽  
Nearly Kaehler Manifold ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold ◽  
Normal Formula

The purpose of this paper is to study normal [Formula: see text]-lightlike submanifolds of indefinite nearly Kaehler manifolds. We find some necessary and sufficient conditions for an isometrically immersed [Formula: see text]-lightlike submanifold of an indefinite nearly Kaehler manifold to be a normal [Formula: see text]-lightlike submanifold. Further, we derive a characterization theorem for holomorphic bisectional curvature of a normal [Formula: see text]-lightlike submanifold of an indefinite nearly Kaehler manifold.

scholarly journals On the geometry of lightlike submanifolds of indefinite statistical manifolds

2020 ◽  
Vol 17 (07) ◽  
pp. 2050099
Author(s):  
Varun Jain ◽  
Amrinder Pal Singh ◽  
Rakesh Kumar
Keyword(s):  
Sectional Curvature ◽  
Classical Theory ◽  
Ricci Tensor ◽  
Statistical Manifolds ◽  
Lightlike Submanifolds ◽  
Statistical Submanifold ◽  
Lightlike Submanifold

We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore, we obtain some conditions for a lightlike submanifold of indefinite statistical manifolds to be a lightlike statistical submanifold. We derive the expression of statistical sectional curvature and finally obtain some conditions for the induced statistical Ricci tensor on a lightlike submanifold of indefinite statistical manifolds to be symmetric.

scholarly journals Screen Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds

2012 ◽  
Vol 52 (4) ◽  
pp. 443-457 ◽  
Author(s):  
S.M. Khursheed Haider ◽  
Advin Advin ◽  
Mamta Thakur
Keyword(s):  
Sasakian Manifolds ◽  
Lightlike Submanifolds

scholarly journals Screen conformal half-lightlike submanifolds

2004 ◽  
Vol 2004 (68) ◽  
pp. 3737-3753 ◽  
Author(s):  
K. L. Duggal ◽  
B. Sahin
Keyword(s):  
Riemannian Manifold ◽  
Sectional Curvature ◽  
Ricci Tensor ◽  
Shape Operator ◽  
Close Relation ◽  
Screen Distribution ◽  
Lightlike Submanifolds ◽  
Half Lightlike Submanifold ◽  
Lightlike Submanifold

We study some properties of a half-lightlike submanifoldM, of a semi-Riemannian manifold, whose shape operator is conformal to the shape operator of its screen distribution. We show that any screen distributionS(TM)ofMis integrable and the geometry ofMhas a close relation with the nondegenerate geometry of a leaf ofS(TM). We prove some results on symmetric induced Ricci tensor and null sectional curvature of this class.

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