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Aug 14, 2014 at 13:54 vote accept Asghar Ghorbanpour
Aug 14, 2014 at 12:41 comment added Asghar Ghorbanpour Ziegler's answer and yours complements each other in the following way. If our compact complex manifold admits any Kahler metric ever, then on can find all the metrics by first fixing a Kahler class in the Kahler cone and then changing the metric in the same class by choosing a smooth function.
Aug 14, 2014 at 2:10 history answered Misha Verbitsky CC BY-SA 3.0