| n维双曲空间和n维球面空间中的正弦定理及应用 |
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| 引用本文： | 王文,杨世国,余静,齐继兵. n维双曲空间和n维球面空间中的正弦定理及应用[J]. 数学杂志, 2014, 34(2): 214-224 |
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| 作者姓名： | 王文 杨世国 余静 齐继兵 |
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| 作者单位： | 合肥师范学院数学系, 安徽 合肥 230601,合肥师范学院数学系, 安徽 合肥 230601,合肥师范学院数学系, 安徽 合肥 230601,合肥师范学院数学系, 安徽 合肥 230601 |
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| 基金项目： | Supported by the Doctoral Programs Foundation of Education Ministry of China (20113401110009);Natural Science Research Project of Hefei Normal University (2012kj11);Uni-versities Natural Science Foundation of Anhui Province (KJ2013A220;KJ2011B133) |
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| 摘 要： | 本文研究了n维双曲空间和n维球面空间中单形的正弦定理和相关几何不等式. 应用距离几何的理论和方法, 给出了n维双曲空间和n维球面空间中一种新形式的正弦定理, 利用建立的正弦定理获得了Hadamard 型和Veljan-Korchmaros型不等式. 另外, 建立了涉及两个n维双曲单形和n维球面单形的"度量加"的一些几何不等式.
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| 关 键 词： | 双曲空间 球面空间 正弦定理 度量加 几何不等式 |
| 收稿时间： | 2012-05-18 |
| 修稿时间： | 2012-11-05 |
THE LAW OF SINES FOR AN n-SIMPLEX IN HYPERBOLIC SPACE AND SPHERICAL SPACE AND ITS APPLICATIONS |
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| WANG Wen,YANG Shi-guo,YU Jing and Qi Ji-bing. THE LAW OF SINES FOR AN n-SIMPLEX IN HYPERBOLIC SPACE AND SPHERICAL SPACE AND ITS APPLICATIONS[J]. Journal of Mathematics, 2014, 34(2): 214-224 |
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| Authors: | WANG Wen YANG Shi-guo YU Jing Qi Ji-bing |
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| Affiliation: | Department of Mathematics, Hefei Normal University, Hefei 230601, China,Department of Mathematics, Hefei Normal University, Hefei 230601, China,Department of Mathematics, Hefei Normal University, Hefei 230601, China and Department of Mathematics, Hefei Normal University, Hefei 230601, China |
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| Abstract: | In this paper, the law of sines and related geometric inequalities for an n-simplex in an n-dimensional hyperbolic space and an n-dimensional spherical space are studied. By using the theory and method of distance geometry, we give the law of sines for an n-simplex in an n-dimensional hyperbolic space and an n-dimensional spherical space. As applications, we obtain Hadamard type inequalities and Veljan-Korchmaros type inequalities in n-dimensional hyperbolic space and n-dimensional spherical space. In addition, some new geometric inequality about"metric addition"involving volume and n-dimensional space angle of simplex in Hn(K) and Sn(K) is established. |
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| Keywords: | hyperbolic space spherical space the law of sine metric addition geometric inequality |
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