Reflection principles for zero mean curvature surfaces in the simply isotropic 3-space

Autor:	Akamine, Shintaro, Fujino, Hiroki
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry Mathematics - Complex Variables Primary 53A10 Secondary 53B30 31A05 31A20
Druh dokumentu:	Working Paper
Popis:	Zero mean curvature surfaces in the simply isotropic 3-space $\mathbb{I}^3$ naturally appear as intermediate geometry between geometry of minimal surfaces in $\mathbb{E}^3$ and that of maximal surfaces in $\mathbb{L}^3$. In this paper, we investigate reflection principles for zero mean curvature surfaces in $\mathbb{I}^3$ as with the above surfaces in $\mathbb{E}^3$ and $\mathbb{L}^3$. In particular, we show a reflection principle for isotropic line segments on such zero mean curvature surfaces in $\mathbb{I}^3$, along which the induced metrics become singular. Comment: 12 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2207.02450 Zobrazit plný text záznamu View this record from Arxiv