A paracomplex structure on a manifold is an endomorphism of the tangent bundle such that , whose -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.
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Costantino Medori, Adriano Tomassini, On small deformations of paracomplex manifolds. J. Noncommut. Geom. 5 (2011), no. 4, pp. 507–522DOI 10.4171/JNCG/84