Cohomological properties of Hermitian symplectic threefolds

Abstract

A Hermitian symplectic manifold is a complex manifold endowed with a symplectic form $\omega$, for which the bilinear form $\omega (I\cdot ,\cdot )$ is positive definite. In this work we prove $d{d}^c$-lemma for 1- and (1,1)-forms for compact Hermitian symplectic manifolds of dimension 3. This shows that Albanese map for such manifolds is well-defined and allows one to prove Kählerness if the dimension of the Albanese image of a manifold is maximal.

8 pages

References in corpus (1)

• Geometry of Hermitian manifolds