Deform a compact Kähler manifold to a non Kähler one - MathOverflow most recent 30 from http://mathoverflow.net2013-06-19T11:26:54Zhttp://mathoverflow.net/feeds/question/47944http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/47944/deform-a-compact-kahler-manifold-to-a-non-kahler-oneDeform a compact Kähler manifold to a non Kähler onediverietti2010-12-01T20:45:40Z2010-12-02T09:46:58Z
<p>Could you give me an example of a compact Kähler manifold which analytically deforms to a non Kähler one?</p>
<p>For example, there is no hope to find a complex structure on a Hopf manifold in order to make it Kähler because of topological obstructions (the second Betti number is zero).</p>
<p>For instance, I think that the Iwasawa manifold should not have topological obstructions.</p>
<p>Of course, the algebraic counterpart of my question has an affirmative answer: complex tori of dimension greater than one give examples of manifolds that can be analytically deformed from an algebraic one to a non algebraic one (but still Kähler). </p>
<p>Thanks in advance!</p>