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

Abstract

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