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Given a compact, connected Lie group G of diffeomorphisms on a manifold M, how to construct a Riemannian metric on M such that elements of G are isometries of M?

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    Fix any Riemann metric on $M$ and average it over the action of $G$.2012-12-04
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    I need compactness for the Haar measure. But can't I do without connectedness?2012-12-04
  • 0
    Connectedness is irrelevant. A compact Lie group has a Haar measure. Just average any Riemann metric over $G$ wrt that measure.2012-12-07

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