Copolarity of isometric actions
Differential Geometry
2007-05-23 v3
Abstract
We introduce a new integral invariant for isometric actions of compact Lie groups, the copolarity. Roughly speaking, it measures how far from being polar the action is. We generalize some results about polar actions in this context. In particular, we develop some of the structural theory of copolarity k representations, we classify the irreducible representations of copolarity one, and we relate the copolarity of an isometric action to the concept of variational completeness in the sense of Bott and Samelson.
Keywords
Cite
@article{arxiv.math/0208105,
title = {Copolarity of isometric actions},
author = {Claudio Gorodski and Carlos Olmos and Ruy Tojeiro},
journal= {arXiv preprint arXiv:math/0208105},
year = {2007}
}
Comments
23 pages, Latex; September17th, 2002: added section 5 and final question 2, added references, and changed subsection 3.3; October 3rd, 2002: new introduction, changes in corollary 5.3 and final question 2