Inequalities for Scalar Curvature and Shape Operator of an R-Lightlike Submanifold in Semi-Riemannian Manifold

A Semi-Riemannian Manifold of Quasi-Constant Curvature with Half Lightlike Submanifolds

In this paper, we study the geometry of a semi-Riemannian manifold M̄ of quasi-constant curvature. The main result is two characterization theorems for M̄ endowed with a statical, screen homothetic or screen totally umbilical half lightlike submanifold M . Mathematics Subject Classification: 53C25, 53C40, 53C50

A Semi-Riemannian Manifold of Quasi-Constant Curvature Admits Lightlike Submanifolds

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we study the geometry of a semi-Riemannian manifold ¯ M of quasi-constant curvature. The main result is two characterization theorems for ¯ M admits solenoidal and screen totally umbilical r (> 1)-lightlike subm...

Lightlike Submanifolds of a Semi-Riemannian Manifold of Quasi-Constant Curvature

A Semi-riemannian Manifold of Quasi-constant Curvature Admits Some Half Lightlike Submanifolds

In this paper, we study the curvature of a semi-Riemannian manifold M̃ of quasi-constant curvature admits some half lightlike submanifolds M . The main result is two characterization theorems for M̃ admits extended screen homothetic and statical half lightlike submanifolds M such that the curvature vector field of M̃ is tangent to M .

Lightlike foliations of semi-Riemannian manifolds1

Using screen distributions and lightlike transversal vector bundles we develop a theory of degenerate foliations of semiRiemannian manifolds. We build lightlike foliations of a semiRiemannian manifold by suspension of a group homomorphism φ : π1(B, x0) → Isom(T ). We compute the basic cohomology groups of the flow determined by a lightlike Killing vector field on a complete semi-Riemannian mani...