论文标题
简单各向同性3空间中零平均曲率表面的反射原理
Reflection principles for zero mean curvature surfaces in the simply isotropic 3-space
论文作者
论文摘要
零平均曲率表面在简单的各向同性3空间$ \ mathbb {i}^3 $自然出现在$ \ mathbb {e}^3 $中的最小表面的几何形状与$ \ mathbb {l} l}^3 $中的最大表面的几何形状。在本文中，我们研究了$ \ mathbb {i}^3 $中零平均曲率表面的反射原理，就像$ \ mathbb {e}^3 $和$ \ mathbb {l}^3 $中的上述表面一样。特别是，我们在$ \ mathbb {i}^3 $中显示了零平均曲率表面的各向同性线段的反思原理，诱导的度量标准变得单数。
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.
