Timeline for Holonomy of compact manifolds
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 16, 2012 at 6:11 | vote | accept | Earthliŋ | ||
| Apr 12, 2012 at 15:14 | comment | added | Robert Bryant | @s.barmeier: No simple way to see it is known that doesn't use some structure theory, both from Lie groups and from de Rham's Theorem. See Besse's comments in Chapter 10, Section E, where the Borel-Lichnerowicz theorem is proved, which states that the identity component of the holonomy of a Riemannian metric is always a closed (and hence compact) subgroup of the orthogonal group. For the effect of the fundamental group, see Section 10.115, but note that this was written before the paper of Wilking appeared, so that particular question is now settled. | |
| Apr 12, 2012 at 13:27 | comment | added | Earthliŋ | So the compactness comes from the type of metric and the simply-connectedness of the manifold, rather than the compactness of the manifold... Is there any way to see this directly and intuitively? | |
| Apr 11, 2012 at 13:54 | history | edited | Robert Bryant | CC BY-SA 3.0 |
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| Apr 11, 2012 at 13:27 | history | answered | Robert Bryant | CC BY-SA 3.0 |