Complete $3$-dimensional $\lambda$-translators in the Minkowski space $\mathbb{R}^{4}_{1}$

Abstract

In this paper, we obtain the classification theorem for three-dimensional complete space-like $\lambda$-translators $x:M^{3} \rightarrow \mathbb R^{4}_{1}$ with constant norm of the second fundamental form and constant $f_{4}$ in the Minkowski space $\mathbb R^{4}_{1}$.