Chen inequalities on lightlike hypersurfaces of a GRW spacetime

Abstract

In this paper, we introduce [Formula: see text]-Ricci curvature and [Formula: see text]-scalar curvature on lightlike hypersurfaces of a GRW spacetime. Using these curvatures, we establish some inequalities for lightlike hypersurfaces of a GRW spacetime. Using these inequalities, we obtain some characterizations on lightlike hypersurfaces. We also get Chen–Ricci inequality and Chen inequality on a screen homothetic lightlike hypersurfaces of a GRW spacetime.

Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms

“…By using the obtained inequality, we derived the Chen inequality for the bi-slant submanifold of generalized Sasakian-space-forms. Recently, Chen inequality for lightlike hypersurfaces of GRW spacetime was obtained by Poyraz [14]. For future research, we would try to combine the methods and results in to obtain the Chen inequalities for submanifolds of indefinite space forms such as spacelike and lightlike.…”

“…Afterward, many authors obtained Chen's inequalities for different submanifolds in various ambient spaces, such as the Kenmotsu space form [4], the Sasakian-space-form [5], the Cosympletic space form [6], the Riemannian manifold of quasi-constant curvature [7], generalized space forms [8,9], Statistical manifolds [10][11][12], quaternionic space forms [13] and the GRW spacetime [14].…”