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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. |
| 关键词: 双曲空间 球面空间 正弦定理 度量加 几何不等式 |
| DOI： |
| 分类号:O184 |
| 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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| 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,Qi Ji-bing
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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. |
| Key words: hyperbolic space spherical space the law of sine metric addition geometric inequality |
