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

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

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

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...

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 .

Inequalities for Submanifolds of a Riemannian Manifold of Nearly Quasi-constant Curvature with a Semi-symmetric Non-metric Connection

By using two new algebraic lemmas we obtain Chen’s inequalities for submanifolds of a Riemannian manifold of nearly quasi-constant curvature endowed with a semi-symmetric non-metric connection. Moreover, we correct a result of C. Özgür and A. Mihai’s paper (Chen inequalities for submanifolds of real space forms with a semi-symmetric non-metric connection, Canad. Math. Bull. 55 (2012), 611–622).