Fixed Points of Isometries
- 1 June 1958
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 13, 63-68
- https://doi.org/10.1017/s0027763000023497
Abstract
The purpose of this paper is to prove the following Theorem. Let M be a Riemannian manifold of dimension n and let ξ be a Killing vector field (i.e., infinitesimal isometry) of M. Let F be the set of points x of M where ξ vanishes and let F = ∪ Vi, where the Vi’s are the connected components of F. Then (assuming F to be non-empty)Keywords
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