论文标题
特征点，基本立方形式和投影表面的Euler特征
Characteristic Points, Fundamental Cubic Form and Euler Characteristic of Projective Surfaces
论文作者
论文摘要
我们在投影3空间中的通用光滑表面上定义了投射脐带和戈德族（也称为高斯的尖）的当地索引。通过这些索引，我们提供了将表面（表面域和表面域上的特征点）代数数与该表面（这些域的分子）的代数数（在表面域上以及表面域上）的代数数。这些关系决定了表面投射的脐带和戈德族的可能共存。我们的研究基于“基本立方形式”，我们为其提供了封闭的简单表达。
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.
