Timeline for How to find special hermitian metrics on vector bundles
Current License: CC BY-SA 2.5
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| Mar 2, 2010 at 10:38 | comment | added | HenrikRüping | In general, whenever one has a compact group acting on a manifold, one can turn a non-invariant Riemannian metric h into a invariant one by averaging over all g*h for g in G. This gives again a Riemannian metric. But I don't think this is, what you were looking for. | |
| Mar 1, 2010 at 21:58 | comment | added | Marty | I've thought about similar things recently. Perhaps this should really be a linear algebra question first! Take $X$ to be a point, so you are simply working with a complex vector space $F$ endowed with a real structure, i.e., a descent datum isomorphism from $F$ to its conjugate space. You want to classify Hermitian forms on $F$ which are compatible, in a sense, with the descent datum. If this is what I think it is, the answer should be something like $GL(F_R) / O(F_R, B)$, where $F_R$ is the conjugation-invariant subspace, and $O(F_R, B)$ is a certain orthogonal group. | |
| Mar 1, 2010 at 21:45 | history | asked | TonyS | CC BY-SA 2.5 |