摘要
在一般的文献中,Poincare-Hopf的曲面奇点指数公式的证明需要利用Euler的曲面示性数公式.本文将通过微分方程的定性方法,直接证明Poincare-Hopf的奇点指数公式,然后作为简单的应用可得到Euler的曲面示性数公式.
In the literature, the Poincare-Hopf's formula for the indeces of singular points is based on the Euler's formula for the characteristic numbers of surfaces. In this paper, we first prove the Poincare-Hopf's formula by means of the emementary methods in the qualitative theory of ordinaray differential equations, and then prove the Euler's formula directly as a corollary.
出处
《数学进展》
CSCD
北大核心
2002年第6期543-548,共6页
Advances in Mathematics（China）
基金
国家自然科学基金资助(No.19731030)
关键词
奇点指数公式
闭曲面
Euler示性数
closed surfaces
index of singular points
Poincare-Hopf's index formula
Euler characteristic number
