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Jul 8, 2011 at 13:58 comment added Francesco Polizzi Ah ok, I did not notice that your complex structure $J$ was fixed. At any rate, I hope you can find this paper useful :-)
Jul 8, 2011 at 13:54 comment added Gunnar Þór Magnússon Thanks Francesco, that's an interesting article. However it does seem to answer a slightly different question. In the notation of the article, we have a fixed complex structure $J$ on $M$ (such that $X = (M,J)$) and ask for structures $(g_1,J,\omega_1)$ and $(g_2, J, \omega_2)$ such that: $g_2 = f^2 g_1$, and ask if the second structure can be Kahler if the first one is and if $f$ is non-constant. In particular, if this is possible, then both structures would induce the same orientation on $M$.
Jul 8, 2011 at 13:34 history undeleted Francesco Polizzi
Jul 8, 2011 at 13:34 history edited Francesco Polizzi CC BY-SA 3.0
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Jul 8, 2011 at 13:32 history deleted Francesco Polizzi
Jul 8, 2011 at 13:27 history answered Francesco Polizzi CC BY-SA 3.0