$d$-Minimal Surfaces in Three-Dimensional Singular Semi-Euclidean Space $\mathbb{R}^{0,2,1}$


  • Yuichiro Sato




minimal surface, isotropic geometry, semi-Riemannian geometry


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 $\mathbb{R}^{4}_{1}$ are in one-to-one correspondence.


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How to Cite

Sato, Y. (2021). $d$-Minimal Surfaces in Three-Dimensional Singular Semi-Euclidean Space $\mathbb{R}^{0,2,1}$. Tamkang Journal of Mathematics, 52(1), 37-67. https://doi.org/10.5556/j.tkjm.52.2021.3045