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.

Conjugate connections with respect to a quadratic endomorphism and duality

“…Let C F (M) be the set of these connections. ii)( [7]) F is a quadratic endomorphism if there exists ε ∈ {−1, +1} such that: F 2 = εI.…”