The Lie group of isometries of a pseudo-Riemannian manifold

被引：0

作者：

Pham, Hung ^{[1
]}

机构：

[1] Victoria Univ Wellington, Sch Math & Stat, Wellington 6140, New Zealand

来源：

ANNALS OF MATHEMATICAL SCIENCES AND APPLICATIONS | 2023年 / 8卷 / 02期

关键词：

Lie group; locally compact group; isometries; pseudo-Riemannian manifold; integral manifold;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give an elementary proof of the Myers-Steenrod theorem, stat-ing that the group of isometries of a connected Riemannian man-ifold M is a Lie group acting smoothly on M. Our proof follows the approach of Chu and Kobayashi, but replacing their use of a theorem of Palais with a topological condition detecting when a locally compact subspace of M is an embedded integral manifold of a given k-plane distribution.

引用

页码：223 / 238

页数：16

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