Chen-like inequalities on lightlike hypersurfaces of a Lorentzian manifold

We introduce k-Ricci curvature and k-scalar curvature on lightlike hypersurfaces of a Lorentzian manifold. We establish some inequalities between the extrinsic scalar curvature and the intrinsic scalar curvature. Using these inequalities, we obtain some characterizations on lightlike hypersurfaces. We give some results with regard to curvature invariants and S(n1, ⋯ , nk)-spaces for lightlike hypersurfaces of a Lorentzian manifold. © 2013 Gülbahar et al.