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 On pinching theorems for compact pseudo-umbilical submanifold

2012 ◽  
Vol 45 (3) ◽  
pp. 645-654
Author(s):  
Jing Mao ◽  
Shaodong Qin
Keyword(s):  
Riemannian Manifold ◽  
Constant Curvature ◽  
Mean Curvature ◽  
Sufficient Conditions ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Parallel Mean Curvature Vector ◽  
Totally Umbilical ◽  
Totally Umbilical Submanifold ◽  
Parallel Mean Curvature

AbstractConsider submanifolds in the nested space. For a compact pseudoumbilical submanifold with parallel mean curvature vector of a Riemannian submanifold with constant curvature immersed in a quasi-constant curvature Riemannian manifold, two sufficient conditions are given to let the pseudo-umbilical submanifold become a totally umbilical submanifold.

scholarly journals Lightlike hypersurfaces of an indefinite Kaehler manifold of a quasi-constant curvature

2019 ◽  
Vol 27 (1) ◽  
pp. 1-12
Author(s):  
Dae Ho Jin ◽  
Jae Won Lee
Keyword(s):  
Vector Field ◽  
Constant Curvature ◽  
Characteristic Vector ◽  
Kaehler Manifold ◽  
Totally Umbilical ◽  
Screen Distribution ◽  
Lightlike Hypersurface ◽  
Lightlike Hypersurfaces ◽  
Characteristic Vector Field

AbstractWe study lightlike hypersurfaces M of an indefinite Kaehler manifold M̅ of quasi-constant curvature subject to the condition that the characteristic vector field ζ of M̅ is tangent to M. First, we provide a new result for such a lightlike hypersurface. Next, we investigate such a lightlike hypersurface M of M̅ such that(1) the screen distribution S(TM) is totally umbilical or(2) M is screen conformal.

scholarly journals On Co-screen Conformality of 1-lightlike Submanifolds in a Lorentzian Manifold

2015 ◽  
Vol 7 (2) ◽  
pp. 76
Author(s):  
Erol Kilic ◽  
Sadik Keles ◽  
Mehmet Gulbahar
Keyword(s):  
Ricci Tensor ◽  
Lorentzian Manifold ◽  
Conformal Killing ◽  
Screen Distribution ◽  
Locally Conformal ◽  
Lightlike Submanifolds

In this paper, the co-screen conformal 1-lightlike submanifolds of a Lorentzian manifoldare introduced as a generalization of co-screen locally half-lightlike submanifolds in(Wang,  Wang {\&} Liu, 2013; Wang {\&} Liu, 2013) and two examples are given whichone is co-screen locally conformal andthe other is not. Some results are obtained on these submanifolds whichthe co-screen distribution is conformal Killing on the ambient manifold.The induced Ricci tensor of  co-screen conformal 1-lightlike submanifolds isinvestigated.

scholarly journals Pseudo-Reimannian manifolds endowed with an almost paraf-structure

1985 ◽  
Vol 8 (2) ◽  
pp. 257-266 ◽  
Author(s):  
Vladislav V. Goldberg ◽  
Radu Rosca
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Mean Curvature ◽  
Integral Manifold ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Minimal Hypersurfaces ◽  
Reimannian Manifolds ◽  
The Mean ◽  
Orthogonal Distribution

LetM˜(U,Ω˜,η˜,ξ,g˜)be a pseudo-Riemannian manifold of signature(n+1,n). One defines onM˜an almost cosymplectic paraf-structure and proves that a manifoldM˜endowed with such a structure isξ-Ricci flat and is foliated by minimal hypersurfaces normal toξ, which are of Otsuki's type. Further one considers onM˜a2(n−1)-dimensional involutive distributionP⊥and a recurrent vector fieldV˜. It is proved that the maximal integral manifoldM⊥ofP⊥hasVas the mean curvature vector (up to1/2(n−1)). If the complimentary orthogonal distributionPofP⊥is also involutive, then the whole manifoldM˜is foliate. Different other properties regarding the vector fieldV˜are discussed.

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 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.

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.

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