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Euler Chracteristics of Surfaces with Negative Curvature
- Euler Chracteristics of Surfaces with Negative Curvature
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- 대학원 수학과
- 이화여자대학교 대학원
- 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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