On Special Calibrated Almost Complex Structures and Moduli Space

Details On Special Calibrated Almost Complex Structures and Moduli Space On Special Calibrated Almost Complex Structures and Moduli Space

2006-06-29

arxiv.org/abs/math/0606759v3

Mathematics

Symplectic Geometry

17 pages

Scientific paper

An \emph{$\omega$-admissible almost complex structure} on a $2n$-dimensional symplectic manifold $(M,\omega)$ is a $\omega$-calibrated almost complex structure $J$ admitting a nowhere vanishing $\bar{\partial}_J$-closed $(n,0)$-form $\psi$. After giving some examples we consider the moduli space of admissible almost complex structures and we study infinitesimal deformations. As special case, we write down explicit computations for the complex torus.

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