Fixed Points of Isometries

説明

<jats:p>The purpose of this paper is to prove the following</jats:p><jats:p>Theorem. <jats:italic>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 = ∪ V<jats:sub>i</jats:sub>, where the V<jats:sub>i</jats:sub>’s are the connected components of F. Then (assuming F to be non-empty</jats:italic>)</jats:p>

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