Copolarity of isometric actions

Details Copolarity of isometric actions Copolarity of isometric actions

2002-08-13

arxiv.org/abs/math/0208105v3

Mathematics

Differential Geometry

23 pages, Latex; September17th, 2002: added section 5 and final question 2, added references, and changed subsection 3.3; Octo

Scientific paper

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.

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