| On the Volume Formulas of Cones and Orthogonal Multi-cones in S^n（1） and H^n（-1） |
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| 作者姓名： | Wu-Yi HSIANG |
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| 作者单位： | [1]Dedicated to the memory of Shiing-Shen Chern [2]Department of Mathematics, The Hong Kong University of Science ＆ Technology, Hong Kong, China; [3]School of Mathematical Sciences, Peking University, Beijing 100871. China. |
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| 摘 要： |
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| 关 键 词： | 双曲线几何 体积公式 正交 凸多面体 |
| 收稿时间： | 15 June 2005 |
On the Volume Formulas of Cones and Orthogonal Multi-cones in $S^n(1)$ and $H^n(-1)$ |
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| Wu-Yi HSIANG.On the Volume Formulas of Cones and Orthogonal Multi-cones in $S^n(1)$ and $H^n(-1)$[J].Chinese Annals of Mathematics,Series B,2006,27(1):1-30. |
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| Authors: | Wu-Yi HSIANG |
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| Institution: | (1) Department of Mathematics, The Hong Kong University of Science & Technology, Hong Kong, China;(2) School of Mathematical Sciences, Peking University, Beijing 100871, China |
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| Abstract: | Abstract In the study of n-dimensional spherical or hyperbolic geometry, n≥ 3, the volume of various objects such as simplexes, convex polytopes, etc. often becomes rather difficult to deal with.
In this paper, we use the method of infinitesimal symmetrization to provide a systematic way of obtaining volume formulas
of cones and orthogonal multiple cones in Sn(1) and Hn(—1).
(Dedicated to the memory of Shiing-Shen Chern) |
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| Keywords: | Hyperbolic geometry Volume |
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