5
votes
1answer
89 views

Explicit description of flat connections under pullback on principal bundles over Riemann surfaces

I'm trying to find a proof/reference for a statement that I've seen quoted in some way or the other, but without reference. The setting: let $P\longrightarrow M$ be a flat principal $G$-bundle over ...
0
votes
0answers
9 views

Short-time representation of variations of metrics on principal bundles via exp?

Let us consider a principal $G$-bundle $P\longrightarrow M$ together with an $H$-reduction $s$, where $H$ is a maximally compact Lie subgroup. As an $H$-reduction, $s\in\Gamma(M,P/H)$, hence we can ...
4
votes
1answer
53 views

“Bundle of metrics” on a principal bundle?

I've come across the term "bundle of metrics" on a principal bundle. In particular, my setting is that for $N\longrightarrow M$ a universal cover of a compact Riemann surface, $P\longrightarrow M$ a ...