论文标题
离散不当仿射球的奇异性
Singularities of Discrete Improper Indefinite Affine Spheres
论文作者
论文摘要
我们在本文中考虑了基于渐近网的离散不当仿射球。在这种情况下，我们区分了必须被认为是单数的离散边缘和顶点。奇异边缘可以视为离散的尖边缘，而某些单数顶点可以被视为离散的燕尾。离散网的奇异性的分类是一项非常困难的任务，我们的结果可以被视为朝这个方向迈出的一步。我们还证明了一些类似于平滑案例的统治不当仿射球的特征。
We consider in this paper discrete improper affine spheres based on asymptotic nets. In this context, we distinguish the discrete edges and vertices that must be considered singular. The singular edges can be considered as discrete cuspidal edges, while some of the singular vertices can be considered as discrete swallowtails. The classification of singularities of discrete nets is a quite difficult task, and our results can be considered as a fisrt step in this direction. We also prove some characterizations of ruled discrete improper affine spheres which are analogous to the smooth case.
