scholarly journals Co-screen conformal half-lightlike submanifolds

2013 ◽  
Vol 44 (4) ◽  
pp. 431-444
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Riemannian Manifold ◽  
Curvature Tensor ◽  
Sufficient Conditions ◽  
Shape Operator ◽  
Geometric Condition ◽  
Screen Distribution ◽  
Unique Existence ◽  
Lightlike Submanifolds ◽  
Half Lightlike Submanifold ◽  
Lightlike Submanifold

In this paper, we introduce and study the geometry of half lightlike submanifold $M$ of a semi-Riemannian manifold $\overline{M}$ satisfying that the shape operator of screen transversal bundle is conformal to the shape operator of lightlike transversal bundle of $M$. Using this geometric condition we obtain some results to characterize the unique existence of screen distribution of $M$, also, we present some sufficient conditions for the induced Ricci curvature tensor of $M$ 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.

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 Some properties of lightlike submanifolds of semi-Riemannian manifolds

2010 ◽  
Vol 43 (3) ◽  
Author(s):  
Rakesh Kumar ◽  
Rachna Rani ◽  
R. K. Nagaich
Keyword(s):  
Riemannian Manifolds ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Totally Geodesic ◽  
Screen Distribution ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

AbstractWe initially obtain various relations and then establish necessary and sufficient condition for the integrability of screen distribution of a lightlike submanifold. We also establish necessary and sufficient condition for a lightlike submanifold to be totally geodesic.

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 Integrability of distributions in CR-lightlike submanifolds

2002 ◽  
Vol 33 (3) ◽  
pp. 209-222
Author(s):  
Bayram Sahin ◽  
Rifat Gunes
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

In this paper, we study CR-lighlike submanifolds of an indefinite Kaehler manifold. Integrability of distributions on CR-lightlike submanifold investigated. We give some necessary and sufficient conditions on integrability of distibutions on CR-lightlike submanifolds in an indefinite Kaehler manifolds.

scholarly journals Half lightlike submanifolds of a semi-Riemannian manifold of quasi-constant curvature

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1737-1745
Author(s):  
Dae Jin ◽  
Jae Lee
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Constant Curvature ◽  
Curvature Vector ◽  
Conformal Killing ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Screen Distribution ◽  
Lightlike Submanifolds

We study the geometry of half lightlike submanifolds (M,g,S(TM), S(TM?)) of a semi-Riemannian manifold (M~,g~) of quasi-constant curvature subject to the following conditions; (1) the curvature vector field ? of M~ is tangent to M, (2) the screen distribution S(TM) of M is either totally geodesic or totally umbilical in M, and (3) the co-screen distribution S(TM?) of M is a conformal Killing distribution.

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 GCR-Lightlike Product of Indefinite Kaehler Manifolds

ISRN Geometry ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Rakesh Kumar ◽  
Sangeet Kumar ◽  
R. K. Nagaich
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We study geodesic -lightlike submanifolds of indefinite Kaehler manifolds and obtain some necessary and sufficient conditions for a -lightlike submanifold to be a -lightlike product.

Geometry of semi-transversal lightlike warped product submanifolds of indefinite Kaehler manifolds

2019 ◽  
pp. 2150001
Author(s):  
Sangeet Kumar
Keyword(s):  
Warped Product ◽  
Shape Operator ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Kaehler Manifold ◽  
Type Formula ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

In this paper, we investigate warped product semi-transversal lightlike submanifolds of indefinite Kaehler manifolds. It is shown that there does not exist any warped product semi-transversal lightlike submanifold of the type [Formula: see text] in an indefinite Kaehler manifold. Moreover, a necessary and sufficient condition for an isometrically immersed semi-transversal lightlike submanifold of an indefinite Kaehler manifold to be a semi-transversal lightlike warped product of the type [Formula: see text] is obtained, in terms of the shape operator.

An investigation on the existence of warped product irrotational screen-real lightlike submanifolds of metallic semi-Riemannian manifolds

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Gauree Shanker ◽  
Ankit Yadav
Keyword(s):  
Riemannian Manifolds ◽  
Design Methodology ◽  
Warped Product ◽  
Sufficient Conditions ◽  
Totally Geodesic ◽  
Content Type ◽  
Lightlike Submanifolds ◽  
Totally Geodesic Foliation ◽  
Is Design ◽  
Lightlike Submanifold

PurposeThe purpose of this paper is to study the geometry of screen real lightlike submanifolds of metallic semi-Riemannian manifolds. Also, the authors investigate whether these submanifolds are warped product lightlike submanifolds or not.Design/methodology/approachThe paper is design as follows: In Section 3, the authors introduce screen-real lightlike submanifold of metallic semi Riemannian manifold. In Section 4, the sufficient conditions for the radical and screen distribution of screen-real lightlike submanifolds, to be integrable and to be have totally geodesic foliation, have been established. Furthermore, the authors investigate whether these submanifolds can be written in the form of warped product lightlike submanifolds or not.FindingsThe geometry of the screen-real lightlike submanifolds has been studied. Also various results have been established. It has been proved that there does not exist any class of irrotational screen-real r-lightlike submanifold such that it can be written in the form of warped product lightlike submanifolds.Originality/valueAll results are novel and contribute to further study on lightlike submanifolds of metallic semi-Riemannian manifolds.

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