Almost invariant submanifolds for compact group actions
微分几何
2007-05-23 v2
摘要
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.
引用
@article{arxiv.math/9908133,
title = {Almost invariant submanifolds for compact group actions},
author = {Alan Weinstein},
journal= {arXiv preprint arXiv:math/9908133},
year = {2007}
}
备注
40 pages, minor corrections and additions