The Riemannian Manifolds with Boundary and Large Symmetry

作     者：Zhi CHEN Yiqian SHI Bin XU Zhi CHEN Yiqian SHI Bin XU Department of Mathematics, University of Science and Technology of China, Hefei 230026, China.

作者机构：Department of Mathematics University of Science and Technology of China Hefei 230026 China. Department of Mathematics University of Science and Technology of China Hefei 230026 China. 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2010年第31卷第3期

页      面：347-360页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Project supported by the National Natural Science Foundation of China (Nos. 10601053, 10671096,10871184, 10971104) Beijing International Mathematical Research Center for the hospitality and financial support during the course of this work 

主　　题：Riemannian manifold with boundary Isometry Rotationally symmetric metric Principal orbit 

摘      要：Seventy years ago, Myers and Steenrod showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. In 2007, Bagaev and Zhukova proved the same result for a Riemannian orbifold. In this paper, the authors first show that the isometry group of a Riemannian manifold M with boundary has dimension at most 1/2 dim M（dim M - 1）. Then such Riemannian manifolds with boundary that their isometry groups attain the preceding maximal dimension are completely classified.