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

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 .

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

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).

Casorati Inequalities for Submanifolds in a Riemannian Manifold of Quasi-Constant Curvature with a Semi-Symmetric Metric Connection

By using new algebraic techniques, two Casorati inequalities are established for submanifolds in a Riemannian manifold of quasi-constant curvature with a semi-symmetric metric connection, which generalize inequalities obtained by Lee et al. J. Inequal. Appl. 2014, 2014, 327.