Ergodic actions of semisimple Lie groups on compact principal bundles

Details Ergodic actions of semisimple Lie groups on compact principal bundles Ergodic actions of semisimple Lie groups on compact principal bundles

2002-05-30

arxiv.org/abs/math/0205323v1

Mathematics

Differential Geometry

15 pages, Latex2e file, no figures

Scientific paper

Let G = SL(n,R) (or, more generally, let G be a connected, noncompact, simple Lie group). For any compact Lie group K, it is easy to find a compact manifold M, such that there is a volume-preserving, connection-preserving, ergodic action of G on some smooth, principal K-bundle P over M. Can M can be chosen independent of K? We show that if M = H/L is a homogeneous space, and the action of G on M is by translations, then P must also be a homogeneous space H'/L'. Consequently, there is a strong restriction on the groups K that can arise over this particular M.

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