Non-embeddability of certain classes of Levi flat manifolds

On the basis of a result of Barrett, we show that members of certain classes of abstract Levi flat manifolds with boundary, whose Levi foliation contains a compact leaf with contracting, flat holonomy, admit no $CR$ embedding as a hypersurface of a complex manifold.Comment: 8 pages, no figure

Bergman spaces of natural G-manifolds

Let G be a unimodular Lie group, X a compact manifold with boundary, and M the total space of a principal bundle G--> M-->X so that M is also a strongly pseudoconvex complex manifold. In this work, we show that if there exists a point p in bM such that T_p(G) is contained in the complex tangent space of bM at p, then the Bergman space of M is large. Natural examples include the gauged G-complexifications of Heinzner, Huckleberry, and Kutzschebauch.Comment: 24 pages, no figure

Infinitesimal and local rigidity of mappings of CR manifolds

A holomorphic mapping $H$ between two real-analytic CR manifolds $M$ and $M'$ is said to be locally rigid if any other holomorphic map $F\colon M \to M'$ which is close enough to $H$ is obtained by composing $H$ with suitable automorphisms of $M$ and $M'$. With the aim of reducing the local rigidity problem to a linear one, we provide sufficient infinitesimal conditions. Furthermore we study some topological properties of the action of the automorphism group on the space of nondegenerate mappings from $M$ to $M'$