Translation hypersurfaces in Lorentz-Minkowski spaces satisfying‎ ‎$L_{n-1}G=AG$

Abstract

In this paper‎, ‎we give a complete classification of the translation hypersurfaces in the‎

‎$(n+1)$-dimensional‎

‎Lorentz-Minkowski space whose Gauss map G satisfies the condition‎

‎$L_{n-1}G=AG$‎

‎where $L_{n-1}$ is the linearized‎

‎operator of the first variation of the the Gauss-Kronecker curvature of the hypersurface and‎

‎$A\in \mathbb{R}^{(n+1)\times(n+1)}$‎

‎is a constant matrix.\\‎

‎\textbf{Keywords:} Gauss-Kronecker curvature‎, ‎Lorentz-Minkowski space‎, ‎Linearized operator $L_{n-1}$‎, ‎Translation hypersurface‎.