| 关于Finsler曲面的几何和拓扑 |
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| 引用本文： | 莫小欢.关于Finsler曲面的几何和拓扑[J].数学进展,1998,27(4):343-350. |
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| 作者姓名： | 莫小欢 |
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| 作者单位： | 北京大学数学学院数学所 |
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| 摘 要： | 本文在Ｆｉｎｓｌｅｒ曲面上定义了一个新的不变量Ｈ。该不变量等于零刻画了Ｒｉｅｍａｎｎ流形。文章给出了Ｈ的一个上界并且构造了Ｈ为常值的非Ｒｉｅｍａｎｎ的Ｆｉｎｓｌｅｒ曲面。此外，本文还推广了Ｌａｎｄｓｂｅｒｇ曲面的Ｇａｕｓ－Ｂｏｎｎｅｔ－Ｃｈｅｒｎ定理并分类了非正曲率的Ｆｉｎｓｌｅｒ曲面。
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| 关 键 词： | Finsler曲面 射影切丛 几何 拓扑 黎曼流形 |
Geometry and Topology on a Finsler Surface |
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| Mo Xiaohuan.Geometry and Topology on a Finsler Surface[J].Advances in Mathematics,1998,27(4):343-350. |
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| Authors: | Mo Xiaohuan |
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| Abstract: | A new invariant H on a Finsler surface, which give a measure of the failure of Finsler surface to be Riemann, is defined. A upper bound of H is obtained. Non-Riemann Finsler surfaces with constant H are constructed. Gauss-Bonnet-Chern theorem for Landsberg surfaces is generalized. A classification of non-positive curved Finsler surfaces is given. |
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| Keywords: | Finlsler surface projectived tangent bundle Gauss-Bonnet-Chern formula Euler characteristic |
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