most recent 30 from http://mathoverflow.net 2013-05-21T08:38:06Z http://mathoverflow.net/feeds/question/24490 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/24490/chern-connection-vs-levi-civita-connection Italo 2010-05-13T10:35:03Z 2010-07-25T23:09:00Z

<p>Hi! I've always read that on a complex manifold (obviously not kahler), with a given hermitian metric on tangent bundle, the chern connection and the levi civita connection on the underlying real bundle could be different. Please can someone give me an explicit example of this fact?</p> <p>Thank you in advance </p>

http://mathoverflow.net/questions/24490/chern-connection-vs-levi-civita-connection/24491#24491 Guangbo Xu 2010-05-13T10:58:52Z 2010-05-13T10:58:52Z

<p>You need a non-Kahler complex manifold. Then the Chern connection will have nontrivial torsion. And the torsion corresponds to the non-closed Kahler form of the metric.</p>

http://mathoverflow.net/questions/24490/chern-connection-vs-levi-civita-connection/33338#33338 Simon Salamon 2010-07-25T23:09:00Z 2010-07-25T23:09:00Z

<p>Further to a previous answer, you might like to refer to <em>arXiv:0911.5655</em> and references therein for some interesting results on Chern connections on non-K&auml;hler (and indeed non-integrable) almost-Hermitian manifolds.</p>