The isometry groups of Riemannian orbifolds
The isometry groups of Riemannian orbifolds
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DOI：
10.1007/s11202-007-0060-y
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发表时间：
2007-07
影响因子：
0.5
通讯作者：
A. V. Bagaev;N. I. Zhukova
中科院分区：
文献类型：
--
作者：
A. V. Bagaev;N. I. Zhukova
本文证明了任意黎曼轨道的等距群<$（）在紧开拓扑的作用下，是一个光滑恰当作用于上的李群，并且<$（）存在唯一的光滑结构使它成为李群.我们特别表明，等距群的每一个紧凑的黎曼orbifold与负定Ricci张量是有限的，从而推广了著名的Bochner定理黎曼流形。
We prove that the isometry group ℑ() of an arbitrary Riemannian orbifold, endowed with the compact-open topology, is a Lie group acting smoothly and properly on. Moreover, ℑ() admits a unique smooth structure that makes it into a Lie group. We show in particular that the isometry group of each compact Riemannian orbifold with a negative definite Ricci tensor is finite, thus generalizing the well-known Bochner’s theorem for Riemannian manifolds.