Maximal compact in conformal group is isometry group

46 Views Asked by Bumbble Comm At 27 Mar 2026 - 7:09

Let $ M $ be a compact Kahler manifold. Then is it true that the maximal compact subgroup of the conformal group is the isometry group?

This seems true for the Riemann surface case.

If $ Conf(M) $ acts transitively on $ M $ does that imply $ Iso(M) $ acts transitively? If not does anyone have a counterexample?

Also

seems to say something about when $ Conf(M)=Iso(M) $ if anyone could help explain it that would be appreciated.

EDIT: Question already answered here, see comments