Distributions associated to almost complex structures on symplectic manifolds

Simone Gutt (Département de Mathématique, Université Libre de Bruxelles, Belgium; and Université de Lorraine, Institut Elie Cartan de Lorraine, Metz, France)

Manar Hayyani (Université Moulay Ismaïl, Meknès, Morocco)

Abstract

We look at methods to select triples $(M,\omega,J)$ consisting of a symplectic manifold $(M,\omega)$ endowed with a compatible positive almost complex structure $J$, in terms of the Nijenhuis tensor $N^J$ associated to $J$. We study the image distribution $\operatorname{Im} N^J$, which is the span at each point of the values of $N^J$, measuring the non integrability of $J$ by the dimension of $\operatorname{Im} N^J$.

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Received 5 March 2020

Accepted 13 October 2020

Published 27 May 2022