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?
2026-05-16 18:24:03.1778955843
Isometries from Diffeomorphisms
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Yes, it is possible without connectedness. You need the fact that the connected component of a Lie Group G that contains the identity of G is a closed, connected normal subgroup of G.