Abstract
This chapter discusses the integrability condition of deformations of CR structures, The parameterization of deformations of a complex manifold by type (1, 0)-valued differential forms of type (0, 1) and the representation of the integrability condition by differential equations on the forms were the keys to open the way to apply the theory of elliptic partial differential equations to deformation theory of complex manifolds. The chapter describes that a similar parameterization and representation can be obtained for CR structures… For the purpose of studying the integrability condition of deformations, a CR structure, denoted by °T" is fixed on M induced by an embedding i:M → N into a complex manifold N of codimension 1 together with a subbundle F ⊂ TM of fiber real dimension 1 such that (°T′ = °T″), providing the expression TM = °T" + °T' + F.
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