$d$-minimal surfaces in three-dimensional singular semi-Euclidean space ${\mathbb{R}}^{0,2,1}$

Abstract

In this paper, we investigate surfaces in singular semi-Euclidean space ${\mathbb{R}}^{0,2,1}$ endowed with a degenerate metric. We define $d$-minimal surfaces, and give a representation formula of Weierstrass type. Moreover, we prove that $d$-minimal surfaces in ${\mathbb{R}}^{0,2,1}$ and spacelike flat zero mean curvature (ZMC) surfaces in four-dimensional Minkowski space ${\mathbb{R}}_1^4$ are in one-to-one correspondence.

24 pages, 10 figures