n维双曲空间和n维球面空间中的正弦定理及应用(英文)  

THE LAW OF SINES FOR AN n-SIMPLEX IN HYPERBOLIC SPACE AND SPHERICAL SPACE AND ITS APPLICATIONS

作　　者：王文[1] 杨世国[1] 余静[1] 齐继兵[1] 

机构地区：[1]合肥师范学院数学系,安徽合肥230601

出　　处：《数学杂志》2014年第2期214-224,共11页Journal of Mathematics

基　　金：Supported by the Doctoral Programs Foundation of Education Ministry of China(20113401110009);Natural Science Research Project of Hefei Normal University(2012kj11);Universities Natural Science Foundation of Anhui Province(KJ2013A220;KJ2011B133)

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.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 H^n（K） and S^n（K） is established.

关 键 词：双曲空间 球面空间 正弦定理 度量加 几何不等式 

分 类 号：O184[理学—数学]