Mathematical Research Letters

Volume 19 (2012)

Number 3

A note on exact forms on almost complex manifolds

Pages: 691 – 697



Tedi Draghici (Department of Mathematics, Florida International University, Miami)

Weiyi Zhang (Department of Mathematics, University of Michigan, Ann Arbor)


On a compact almost complex manifold $(M^{2n},J)$, theconditions that $J$ admits tamed or compatible symplectic forms are characterized in termsof exact forms. In dimension 4, it is shown that $J$ admits acompatible symplectic form if and only if $J$ admitstamed symplectic forms with arbitrary $J$-anti-invariant parts.

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