most recent 30 from http://mathoverflow.net 2013-05-26T01:34:11Z http://mathoverflow.net/feeds/question/94825 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/94825/isomorphism-type-of-holomorphic-structures google 2012-04-22T09:06:57Z 2012-04-22T09:06:57Z

<p>Let F be smooth complex bundle with flat connection D. Let H be hermitian metric, D not nec. compatible with H. FACT: There is another connection DD, commpatible with H, such that (1,0) form of (D-DD) and (0,1) form of (D-DD) are adjoint concerning H. Question: Assume DD^2 has zero (0,2)-part. When are the holomorphic structures given by by DD^(0,1) and D^(0,1) isomorphic ?</p>