| 关于亏格大于零的紧致黎曼曲面上的割迹 |
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| 引用本文： | 许洪伟.关于亏格大于零的紧致黎曼曲面上的割迹[J].上海师范大学学报(自然科学版),1987(2). |
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| 作者姓名： | 许洪伟 |
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| 作者单位： | 华东师范大学数学系 |
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| 摘 要： | S.B.Myers 证明了对亏格为零的紧致黎曼曲面的割迹 C(p)上任一点 q,在作为有限单纯复形的 C(p)中从 q 点出发的一维胞腔的数目等于从 p 到 q 的极小测地线的数目。用新的方法改进了其证明。本文证明了对亏格大于零的情形,相应的结论仍然成立。
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| 关 键 词： | 亏格 紧致黎曼曲面 割迹 极小测地线 指数映照 |
Cut Locus on a Compact Riemannian Surface with Positive Genus |
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| XU HONGWEI.Cut Locus on a Compact Riemannian Surface with Positive Genus[J].Journal of Shanghai Normal University(Natural Sciences),1987(2). |
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| Authors: | XU HONGWEI |
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| Institution: | Department of Mathematics |
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| Abstract: | The cut locus for a compact Riemannian surface of genus zero was discussed by S. B.Myers in1]and improved by Zhou Kexi in2].When the genus is n>0,a similar result that on a compact Riemannian surface,as a cut point,the order of a point in a cut locus is equal to its order as a vertex of the complex,is given in this paper. |
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| Keywords: | genus compact Riemannian surface cut locus minimal geodesic exponential map |
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