On orbit spaces of representations of compact Lie groups

Details On orbit spaces of representations of compact Lie groups On orbit spaces of representations of compact Lie groups

2011-09-08

arxiv.org/abs/1109.1739v1

Mathematics

Differential Geometry

Scientific paper

We investigate classes of orthogonal representations of compact Lie groups that have isometric orbit spaces. We find invariants and general structural results of such classes. Our main technical result provides a geometric description of classes which contain representations with very different algebraic properties. Such classes contain most representations arising naturally in geometric problems, for instance, representations of low copolarity and most representations of low cohomogeneity.

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