Abstract
In this note, we prove and discuss the following theorem: if the symplectic or almost symplectic manifoldM admits a nice polarizationF with dim\((F \cap \bar F) = k \ne 0\), we must have Chernq M=0 and Pontq M=0, forq>2n−k, and, in particular, the Euler class ofM vanishes.
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Vaisman, I. The Bott obstruction to the existence of nice polarizations. Monatshefte für Mathematik 92, 231–238 (1981). https://doi.org/10.1007/BF01442487
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DOI: https://doi.org/10.1007/BF01442487