Some inequalities on screen homothetic lightlike hypersurfaces of a Lorentzian manifold (Q395643)

The authors introduce the concept of screen homothetic light-like hypersurfaces in a Lorentzian manifold, then they establish some inequalities of B. Y. Chen's style for this kind of hypersurfaces and give some characterizations using these inequalities. As an example, one of these results is the followingNEWLINENEWLINENEWLINE{Theorem 3.4} Let \(M\) be a screen homothetic light-like hypersurface with \(\varphi>0\) of a Lorentzian space form \(\widetilde{M}(c)\). Then we have NEWLINE\[NEWLINE \tau(p)\leq n^2c+\varphi\{n(n-1)\mu^2\},NEWLINE\]NEWLINE where \(\tau\) is the scalar curvature of \(M\) and \(\mu\) is the mean curvature of \(M\). The equality holds for \(p\in M\) if and only if \(p\) is a totally umbilical point.NEWLINENEWLINENEWLINEA former paper of the authors is [J. Inequal. Appl. 2013, Article ID 266, 18 p. (2013; Zbl 1283.53020)].