Strictly pseudoconvex b-CR manifolds

A b-CR structure on a smooth (2n + 1)-manifold M with boundary is an involutive subbundle V of the complexification of the b-tangent bundle of M such that V boolean AND (V) over bar = {0} and the codimension of V circle plus (V) over bar in (CT)-T-b M is 1. This class of manifolds and structures contains the spherical blowups at singular points of hypersufaces in Cn+1 with conical singular points. Suppose M is compact. Under strict pseudoconvexity conditions we investigate properties of the restriction of V to the boundary of M, prove the finite-dimensionality of the cohomology groups in degrees 1 less than or equal to q less than or equal to n - 1 for various natural complexes of operators on M, and prove an embedding theorem of M in some C-N assuming additional conditions on the boundary structure.