Timeline for Fibre metrics on non-linear bundles
Current License: CC BY-SA 4.0
2 events
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| Oct 16, 2020 at 10:13 | comment | added | Sebastian Goette | This situation arises in family index theory. If you have a fibrewise metric and a splitting $TY=T^vY\oplus T^hY$ with $T^vY=\ker d\pi$ and $T^hY\cong\pi^*TX$, then there is a natural connection (due to Bismut) on the bundle $T^vY\to Y$ that restricts to the Levi-Civita connection on each fibre. This is discussed in the book by Berline, Getzler and Vergne in Section 10.1. Is that what you are looking for? | |
| Oct 15, 2020 at 15:55 | history | asked | Bence Racskó | CC BY-SA 4.0 |