Almost analytic forms with respect to a quadratic endomorphism and their cohomology


Abstract: The goal of this paper is to consider the notion of almost analytic form in a unifying setting for both almost complex and almost paracomplex geometries. We use a global formalism, which yields, in addition to generalizations of the main results of the previously known almost complex case, a relationship with the Frölicher-Nijenhuis theory. A cohomology of almost analytic forms is also introduced and studied as well as deformations of almost analytic forms with pairs of almost analytic functions.

Keywords: Quadratic endomorphism, almost $F$-analytic form, $F$-symmetric form, almost (para)complex structure, cohomology

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