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Nov 28, 2015 at 23:45 comment added Misha Igor, your references do not really resolve the question which OP is asking. The issue of integrability of the almost complex structure is a delicate one: For the loop space of a 3-dimensional Riemannian manifold (the case I thought about) the answer is that the almost complex structure is formally integrable but, in general, not integrable, see Lempert's paper. What happens when the target is Kahler I am not sure.
Nov 28, 2015 at 18:39 comment added Igor Rivin @MeerAshwinkumar An even more explict description is in the second reference...
Nov 28, 2015 at 18:38 history edited Igor Rivin CC BY-SA 3.0
added reference
Nov 28, 2015 at 17:01 comment added Meer Ashwinkumar Could you kindly point out the section I should be looking for, I can't seem to find it.
Nov 28, 2015 at 17:00 vote accept Meer Ashwinkumar
Nov 29, 2015 at 3:14
Nov 28, 2015 at 16:52 history answered Igor Rivin CC BY-SA 3.0