On Cohomological Decomposition of Almost-Complex Manifolds and Deformations

Details On Cohomological Decomposition of Almost-Complex Manifolds and Deformations On Cohomological Decomposition of Almost-Complex Manifolds and Deformations

2009-09-19

arxiv.org/abs/0909.3604v1

Mathematics

Differential Geometry

20 pages

Scientific paper

While small deformations of K\"ahler manifolds are K\"ahler too, we prove that the cohomological property to be \Cpf is not a stable condition under small deformations. This property, that has been recently introduced and studied by T.-J. Li and W. Zhang in \cite{li-zhang} and T. Draghici, T.-J. Li and W. Zhang in \cite{draghici-li-zhang, draghici-li-zhang1}, is weaker than the K\"ahler one and characterizes the almost-complex structures that induce a decomposition in cohomology. We also study the stability of this property along curves of almost-complex structures constructed starting from the harmonic representatives in special cohomology classes.

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