Almost invariant submanifolds for compact group actions

Details Almost invariant submanifolds for compact group actions Almost invariant submanifolds for compact group actions

1999-08-25

arxiv.org/abs/math/9908133v2

Mathematics

Differential Geometry

40 pages, minor corrections and additions

Scientific paper

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.

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