Some characterizations on minimal lightlike submanifolds

2017 ◽  
Vol 14 (07) ◽  
pp. 1750103 ◽  
Author(s):  
Sangeet Kumar
Keyword(s):  
Sectional Curvature ◽  
Ricci Tensor ◽  
Minimal Condition ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

The present paper deals with the study of minimal lightlike submanifolds. We investigate a class of lightlike submanifolds namely, generic lightlike submanifolds under the minimal condition. We give one nontrivial example for minimal generic lightlike submanifolds and derive some characterization theorems for a generic lightlike submanifold to be a minimal lightlike submanifold. We also establish some conditions for the distributions for generic lightlike submanifolds to be minimal. We further derive the expressions for sectional curvature, null sectional curvature and induced Ricci tensor for a minimal lightlike submanifold. Finally, we prove that for a minimal lightlike submanifold, the null sectional curvature vanishes and the induced Ricci tensor is symmetric.

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 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.

scholarly journals Characterization of Holomorphic Bisectional Curvature ofGCR-Lightlike Submanifolds

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Sangeet Kumar ◽  
Rakesh Kumar ◽  
R. K. Nagaich
Keyword(s):  
Sectional Curvature ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Holomorphic Sectional Curvature ◽  
Bisectional Curvature ◽  
Holomorphic Bisectional Curvature ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of aGCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature ofGCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for aGCR-lightlike submanifold of an indefinite complex space form to be null holomorphically flat. We also obtain some characterization theorems for holomorphic sectional and holomorphic bisectional curvature.

Some characterization theorems on holomorphic sectional curvature of GCR-lightlike submanifolds

2017 ◽  
Vol 14 (03) ◽  
pp. 1750034 ◽  
Author(s):  
Varun Jain ◽  
Rachna Rani ◽  
Rakesh Kumar ◽  
R. K. Nagaich
Keyword(s):  
Sectional Curvature ◽  
Sasakian Manifold ◽  
Holomorphic Sectional Curvature ◽  
Bisectional Curvature ◽  
Holomorphic Bisectional Curvature ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Sasakian manifold and obtain some characterization theorems on holomorphic sectional and holomorphic bisectional curvature.

Radical screen transversal lightlike submanifolds of indefinite Kaehler manifolds admitting a quarter-symmetric non-metric connection

2018 ◽  
Vol 15 (02) ◽  
pp. 1850024
Author(s):  
Garima Gupta ◽  
Rakesh Kumar ◽  
Rakesh Kumar Nagaich
Keyword(s):  
Product Manifold ◽  
Necessary And Sufficient Condition ◽  
Kaehler Manifold ◽  
Screen Distribution ◽  
Kaehler Manifolds ◽  
Metric Connection ◽  
Necessary And Sufficient ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We study radical screen transversal ([Formula: see text])-lightlike submanifolds of an indefinite Kaehler manifold admitting a quarter-symmetric non-metric connection and obtain a necessary and sufficient condition for the screen distribution of a radical [Formula: see text]-lightlike submanifold to be integrable. We also study totally umbilical radical [Formula: see text]-lightlike submanifolds and obtain some characterization theorems for a radical [Formula: see text]-lightlike submanifold to be a lightlike product manifold. Finally, we establish some results regarding the vanishes of null sectional curvature.

scholarly journals Totally contact umbilical slant lightlike submanifolds of indefinite Kenmotsu manifolds

2015 ◽  
Vol 46 (2) ◽  
pp. 179-191
Author(s):  
Rashmi Schdeva ◽  
Rakesh Kumar ◽  
Satvinder Singh Bhatia
Keyword(s):  
Space Forms ◽  
Kenmotsu Manifolds ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

In this paper, we study totally contact umbilical slant lightlike submanifolds of indefinite Kenmotsu manifolds. We prove that there does not exist totally contact umbilical proper slant lightlike submanifold in indefinite Kenmotsu manifolds other than totally contact geodesic proper slant lightlike submanifold. We also prove that there does not exist totally contact umbilical proper slant lightlike submanifold of indefinite Kenmotsu space forms. Finally, we give some characterization theorems on minimal slant lightlike submanifolds of indefinite Kenmotsu manifolds.

Screen slant lightlike submanifolds of indefinite cosymplectic manifolds

2011 ◽  
Vol 18 (1) ◽  
pp. 83-97
Author(s):  
Ram Shankar Gupta
Keyword(s):  
Characterization Theorem ◽  
Cosymplectic Manifold ◽  
Cosymplectic Manifolds ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

Abstract In this paper, we introduce the notion of a screen slant lightlike submanifold of an indefinite cosymplectic manifold. We provide a characterization theorem for the existence of a screen slant lightlike submanifold with examples. Also, we give an example of a minimal screen slant lightlike submanifold of and prove some characterization theorems.

scholarly journals Hemi-Slant Lightlike Submanifolds of Indefinite Kenmotsu Manifolds

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
S. M. Khursheed Haider ◽  
Mamta Thakur ◽  
Advin
Keyword(s):  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Metric Connection ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We introduce and study hemi-slant lightlike submanifolds of an indefinite Kenmotsu manifold. We give an example of hemi-slant lightlike submanifold and establish two characterization theorems for the existence of such submanifolds. We prove some theorems which ensure the existence of minimal hemi-slant lightlike submanifolds and obtain a condition under which the induced connection ∇ on M is a metric connection. An example of proper minimal hemi-slant lightlike submanifolds is also given.

scholarly journals OnGCR-Lightlike Product of Indefinite Cosymplectic Manifolds

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Varun Jain ◽  
Rakesh Kumar ◽  
R. K. Nagaich
Keyword(s):  
Cosymplectic Manifolds ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We defineGCR-lightlike submanifolds of indefinite cosymplectic manifolds and give an example. Then, we study mixed geodesicGCR-lightlike submanifolds of indefinite cosymplectic manifolds and obtain some characterization theorems for aGCR-lightlike submanifold to be aGCR-lightlike product.

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.

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