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Jan 1, 2013 at 7:12 comment added Atsushi Kanazawa You may be interested in a similar question mathoverflow.net/questions/110613/…
Dec 31, 2012 at 20:35 vote accept T Wong
Dec 31, 2012 at 16:43 comment added Mark Gross As Robert points out, it is easy to find examples where the holonomy group is not all of $SU(3)$, such as a product of a K3 surface and an elliptic curve, or quotients thereof where the metric is an orbifold metric. But there are still no compact examples with full $SU(3)$ holonomy. It would be nice to see further progress on this problem.
Dec 31, 2012 at 13:39 comment added Allen Mark Gross is an expert in this field. By the way, as far as I know consturcting a special Lag submanifold on a compact CY3 is too difficult, not to say you want a special Lag fibration. This is the reason why many people now only consider Lag fibration for the purpose of mirror symmetry.
Dec 31, 2012 at 13:25 answer added Robert Bryant timeline score: 3
Dec 31, 2012 at 7:37 history asked T Wong CC BY-SA 3.0