Rigidity theorems of the space-like $\lambda$-hypersurfaces in the Lorentzian space ${\mathbb{R}}_1^{n+1}$

Abstract

In this paper, we study complete space-like $\lambda$-hypersurfaces in the Lorentzian space ${\mathbb{R}}_1^{n+1}$. As the result, we prove some rigidity theorems for these hypersurfaces including the complete space-like self-shrinkers in $\bbr^{n+1}_1$.

submitted