Timeline for HyperKaehler manifolds are Ricci-flat
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 25, 2012 at 3:22 | comment | added | YangMills | calvino.polito.it/~salamon/G/rghg.pdf | |
| Oct 24, 2012 at 17:26 | comment | added | Paul Reynolds | It's called "Riemannian Geometry and Holonomy Groups". I've just had a look and unfortunately it no longer appears to be on his website. If you can get hold of a copy I'd strongly recommend it. | |
| Oct 24, 2012 at 17:22 | comment | added | Mina | what is the title of salamon's red book ? | |
| Oct 24, 2012 at 16:58 | comment | added | diverietti | Right, sorry I got confused on that point. There are anyway some troubles in the question. | |
| Oct 24, 2012 at 16:56 | comment | added | Paul Reynolds | Actually $\omega_c$ is $I$-holomorphic, see p398 of Besse. Hyperkaehler manifolds are Ricci flat because they are special cases of Calabi-Yau manifolds. My favourite book on this is Salamon's little red book, which I believe is free from his website. | |
| Oct 24, 2012 at 16:26 | comment | added | diverietti | I think your question have some problems. First, $\omega_c$ is a $(1,1)$-form, so $\omega_c^n$ is not a holomorphic form nor a trivializing section of the canonical bundle. Next, a manifold is not Ricci flat with respect to a form... Anyway, if the canonical bundle is trivial or, more generally, if the first real Chern class vanishes, then Yau's solution of the Calabi conjecture provide a Kähler metric which is Ricci flat. | |
| Oct 24, 2012 at 15:54 | history | asked | Mina | CC BY-SA 3.0 |