Timeline for connections on principal bundles over $S^1$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 3, 2014 at 22:45 | vote | accept | user47719 | ||
| Mar 3, 2014 at 22:08 | comment | added | Robert Bryant | Because $G$ is compact, it has a bi-invariant metric and the geodesics of such a metric are the 1-parameter subgroups. Since the exponential map from a point is onto when the manifold is compact, and since the diameter of $G$ is bounded, there is a upper bound $D$ on the length of a minimizing geodesic. Now let $K$ be the set of vectors in $\frak{g}$ of length at most $D/(2\pi)$. | |
| Mar 3, 2014 at 19:42 | comment | added | user47719 | Thanks! So what I was missing is your last statement. I know it is true but how can I prove the existence of the compact set $K$? | |
| Mar 3, 2014 at 12:18 | history | answered | Robert Bryant | CC BY-SA 3.0 |