Timeline for Berger's theorem on Riemannian holonomy applied to the orthogonal frame bundle.
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 15, 2012 at 18:31 | comment | added | Pablo Lessa | Once again, Thanks! This is great! | |
| Nov 15, 2012 at 13:09 | comment | added | Robert Bryant | @Pablo: Yes, it is now known that there are many examples of each kind, except in Case 8, where the only examples are locally equivalent to either the Cayley plane $\mathbb{OP}^2$ and its noncompact dual. One reference (though there are, of course, very many) is my survey article Classical, exceptional, and exotic holonomies: a status report, in Actes de la Table Ronde de Géométrie Différentielle (Luminy, 1992), Sémin. Congr., vol. 1 (1996), pp. 93–165, Soc. Math. France, Paris. The action in all cases is the lowest dimensional faithful representation of that group. | |
| Nov 15, 2012 at 10:40 | comment | added | Pablo Lessa | Also: examples 2 and 3 are complex matrix groups, What is the action on $\mathbb{R}^n$ under consideration? | |
| Nov 15, 2012 at 10:32 | comment | added | Pablo Lessa | Thanks! Are there examples in each class? Any references? | |
| Nov 15, 2012 at 10:27 | vote | accept | Pablo Lessa | ||
| Nov 14, 2012 at 19:53 | history | answered | Robert Bryant | CC BY-SA 3.0 |