Almost invariant submanifolds for compact group actions

Alan Weinstein

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arxiv math/9908133 v2 pith:UNZWS5DH submitted 1999-08-25 math.DG

Almost invariant submanifolds for compact group actions

Alan Weinstein This is my paper

classification math.DG

keywords submanifoldscompactaveraginggroupprocedureriemanniansubmanifoldaction

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We define a C^1 distance between submanifolds of a riemannian manifold M and show that, if a compact submanifold N is not moved too much under the isometric action of a compact group G, there is a G-invariant submanifold C^1-close to N. The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney's idea of realizing submanifolds as zeros of sections of extended normal bundles.

Almost invariant submanifolds for compact group actions

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