Characteristic Points, Fundamental Cubic Form and Euler Characteristic of Projective Surfaces

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2020-05-07 DOI:10.17323/1609-4514-2020-20-3-511-530

M. Kazarian, R. Uribe-Vargas

引用次数: 4

Abstract

We define local indices for projective umbilics and godrons (also called cusps of Gauss) on generic smooth surfaces in projective 3-space. By means of these indices, we provide formulas that relate the algebraic numbers of those characteristic points on a surface (and on domains of the surface) with the Euler characteristic of that surface (resp. of those domains). These relations determine the possible coexistences of projective umbilics and godrons on the surface. Our study is based on a "fundamental cubic form" for which we provide a closed simple expression.

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射影曲面的特征点、基本三次形式和欧拉特征

我们定义了投影3-空间中一般光滑表面上的投影脐和Godron（也称为高斯尖）的局部指数。通过这些指数，我们提供了将曲面上（和曲面的域上）那些特征点的代数数与该曲面的欧拉特征（分别是这些域）联系起来的公式。这些关系决定了投影脐和Godron在曲面上可能共存。我们的研究基于“基本立方形式”，我们为其提供了一个封闭的简单表达式。

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

Moscow Mathematical Journal 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.