The principal investigator will study the problem of imbedding three dimensional CR manifolds into Euclidean space. He will approach the problem of imbeddibility of CR manifolds in terms of a moduli space and attempt to describe those CR manifolds which are imbeddible by relating the problem to a circle action on the boundary of a convex domain. In particular he will try to understand how the circle action changes when the CR structure is perturbed. A CR manifold is an important abstract structure in the geometry of spaces of complex numbers. To better understand these spaces one would like to visualize them as subspace of the usual Euclidean space such as our everyday three dimensional space. The principal investigator will attempt to describe when this visualization or "imbedibility" is possible.
