离散不定仿射极小曲面的奇点

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2024-11-12 DOI:10.1016/j.difgeo.2024.102206

Marcos Craizer

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引用次数: 0

摘要

根据勒里厄尔公式，可以从一对平滑的非相交空间曲线得到具有不定度量的平滑仿射极小曲面。这些曲面可能会出现奇点，一般是尖顶边缘和燕尾形。通过将初始曲线离散化，可以用离散的勒里厄尔公式得到具有不定度量的离散仿射极小曲面。本文的目的是定义相应离散渐近网的奇异边和顶点，从而使光滑版本奇异集的最相关特性保持有效。

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Singularities of discrete indefinite affine minimal surfaces

A smooth affine minimal surface with indefinite metric can be obtained from a pair of smooth non-intersecting spatial curves by Lelieuvre's formulas. These surfaces may present singularities, which are generically cuspidal edges and swallowtails. By discretizing the initial curves, one can obtain by the discrete Lelieuvre's formulas a discrete affine minimal surface with indefinite metric. The aim of this paper is to define the singular edges and vertices of the corresponding discrete asymptotic net in such a way that the most relevant properties of the singular set of the smooth version remain valid.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.