On small deformations of paracomplex manifolds

A paracomplex structure on a manifold M is an endomorphism K of the tangent bundle TM such thatK D I , whose ̇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. Mathematics Subject Classification (2010). 53C15, 32G07.