Almost invariant submanifolds for compact group actions

Weinstein, Alan. "Almost invariant submanifolds for compact group actions." Journal of the European Mathematical Society 002.1 (2000): 53-86. <http://eudml.org/doc/277434>.

@article{Weinstein2000,
abstract = {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.},
author = {Weinstein, Alan},
journal = {Journal of the European Mathematical Society},
keywords = {distance between submanifolds; invariant submanifold; riemannian manifold; -manifold; invariant submanifold; distance between submanifold},
language = {eng},
number = {1},
pages = {53-86},
publisher = {European Mathematical Society Publishing House},
title = {Almost invariant submanifolds for compact group actions},
url = {http://eudml.org/doc/277434},
volume = {002},
year = {2000},
}

TY - JOUR
AU - Weinstein, Alan
TI - Almost invariant submanifolds for compact group actions
JO - Journal of the European Mathematical Society
PY - 2000
PB - European Mathematical Society Publishing House
VL - 002
IS - 1
SP - 53
EP - 86
AB - 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.
LA - eng
KW - distance between submanifolds; invariant submanifold; riemannian manifold; -manifold; invariant submanifold; distance between submanifold
UR - http://eudml.org/doc/277434
ER -