A generalization of the normal holomorphic frames in symplectic manifolds
In this paper we give a generalization of the normal holomorphic frames in symplectic manifolds and find conditions for the integrability of complex structures.
On the Calabi-Yau equation in the Kodaira-Thurston manifold
We review some previous results about the Calabi-Yau equation on the Kodaira-Thurston manifold equipped with an invariant almost-Kähler structure and assuming the volume form T2-invariant. In particular, we observe that under some restrictions the problem is reduced to aMonge-Ampère equation by using the ansatz ˜~ω = Ω− dJdu + da, where u is a T2-invariant function and a is a 1-form depending on u. Furthermore, we extend our analysis to non-invariant almost-complex structures by considering some...
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