Minimal homothetical and translation lightlike graphs in $ \mathbb{R} _{q}^{n+2} $

Abstract

In this paper, homothetical and translation lightlike graphs, which are generalizations of homothetical and translation lightlike hypersurfaces are investigated in the semi-Euclidean space $ \mathbb{R}_{q}^{n+2} $, respectively. We prove that all homothetical and all translation lightlike graphs are locally the hyperplanes. According to this fact, both of these graphs are minimal.

Keywords

• lightlike hypersurfaces
• homothetical graphs
• translation graphs
• semi-euclidean space
• minimality