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Euler Chracteristics of Surfaces with Negative Curvature

Title
Euler Chracteristics of Surfaces with Negative Curvature
Authors
劉点志
Issue Date
2004
Department/Major
대학원 수학과
Publisher
이화여자대학교 대학원
Degree
Master
Advisors
조용승
Abstract
In this paper,we show that the influence of Gaussian curvature penetrates to the topological conformation of M, when it is a surface in R³- to properties independent of the geometry of M. We introduce the Gauss-Bonnet Theorem on compact oriented surfaces and its applications. Finally, we show that a compact surface has negative Euler characteristic if and only if it admits a metric of constant negative curvature.
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일반대학원 > 수학과 > Theses_Master
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