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Questions about Kähler manifolds and Kähler metrics.
9
votes
Examples of non-Kahler compact symplectic manifolds.
There are lots of simply-connected four-dimensional examples in Gompf's symplectic sum paper paper which are shown to be non-Kahler by virtue of violating the Noether inequality (see Theorem 6.2). Th …
7
votes
Compact Kaehler manifolds that are isomorphic as symplectic manifolds but not as complex man...
In case anybody is curious, there are still examples of (1) even if one replaces the requirement that the complex manifolds be nonisomorphic with the requirement that they be not even deformation equi …