On deformations of D-manifolds and CR D-manifolds

In this paper we study the problem of small deformations of D-structures on compact manifolds. We prove that the integrability condition, namely the classical Maurer–Cartan equation, can be viewed as a condition on the space of skew-symmetric derivations of the algebra ∧K0,∗(M). The last part of the paper is devoted to the study of small deformations of strictly CR D-manifolds, and we consider explicit examples of such CR D-manifolds.