Timeline for Intuition about covariant derivative/connections on real and complex manifolds
Current License: CC BY-SA 3.0
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| Dec 18, 2013 at 14:58 | comment | added | Deane Yang | I haven't looked at Kobayashi-Nomizu in decades, but I'd be surprised if it doesn't define curvature using the definition of a connection you cite. In any case, it's easy to guess what it is, since a connection is flat if and only if the distribution is integrable. Probably the easiest way to verify this is by differentiating the Lie algebra-valued connection 1-form. Torsion is defined only if the principal fiber bundle is a subbundle of tangent frame bundle. Not sure how that translates. And what do you mean by symmetry? That's usually a synonym for torsion-free. | |
| Dec 18, 2013 at 4:54 | history | answered | JHM | CC BY-SA 3.0 |