具有边界和大对称性的黎曼流形
微分几何
2009-05-11 v3
摘要
六十年前，S. B. Myers 和 N. E. Steenrod ({\it Ann. of Math.} {\bf 40} (1939), 400-416) 证明了无边界黎曼流形的等距群具有李群结构。最近，A. V. Bagaev 和 N. I. Zhukova ({\it Siberian Math. J.} {\bf 48} (2007), 579-592) 对黎曼轨形证明了相同的结果。在本文中，我们首先证明具有边界的黎曼流形 的等距群维数至多为 。随后，我们完全分类了那些等距群达到前述最大维数的具有边界的黎曼流形。
引用
@article{arxiv.0801.0948,
title = {The Riemannian manifolds with boundary and large symmetry},
author = {Zhi Chen and Yiqian Shi and Bin Xu},
journal= {arXiv preprint arXiv:0801.0948},
year = {2009}
}
备注
The former paper has been replaced by a substantially revised version. Title also changed