Chen-like inequalities on null hypersurfaces with closed rigging of a Lorentzian manifold

Abstract

We study null hypersurfaces of a Lorentzian manifold with a closed rigging for the hypersurface. We derive inequalities involving Ricci tensors, scalar curvature, squared mean curvatures for a null hypersurface with a closed rigging of a Lorentzian space form and for a screen homothetic null hypersurface of a Lorentzian manifold. We also establish a generalized Chen–Ricci inequality for a screen homothetic null hypersurface of a Lorentzian manifold with a closed rigging for the hypersurface.