On Gaussian curvatures and singularities of Gauss maps of cuspidal edges

IF 0.5 4区数学 Q3 MATHEMATICS

Portugaliae Mathematica Pub Date : 2020-03-24 DOI:10.4171/pm/2065

Keisuke Teramoto

引用次数: 2

Abstract

We show relation between sign of Gaussian curvature of cuspidal edge and geometric invariants through types of singularities of Gauss map. Moreover, we define and characterize positivity/negativity of cusps of Gauss maps by geometric invariants of cuspidal edges, and show relation between sign of cusps and of the Gaussian curvature.

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关于高斯曲率和高斯倒钩边映射的奇异性

通过高斯映射的奇点类型，给出了尖边高斯曲率的符号和几何不变量之间的关系。此外，我们还利用尖边的几何不变量定义和刻画了高斯映射尖点的正负性，并给出了尖点符号和高斯曲率符号之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Portugaliae Mathematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： Since its foundation in 1937, Portugaliae Mathematica has aimed at publishing high-level research articles in all branches of mathematics. With great efforts by its founders, the journal was able to publish articles by some of the best mathematicians of the time. In 2001 a New Series of Portugaliae Mathematica was started, reaffirming the purpose of maintaining a high-level research journal in mathematics with a wide range scope.