On small deformations of paracomplex manifolds

Abstract

A paracomplex structure on a manifold $M$ is an endomorphism $K$ of the tangent bundle $TM$ such that $K^2= I$, whose $\pm 1$-eigenspaces have the same dimension and are involutive. By using the theory of differential graded Lie algebras, we describe small deformations of paracomplex structures. We also compute the space of invariant small deformations of 4-dimensional nilmanifolds endowed with a fixed paracomplex structure.