UC San Diego

This work will concentrate on transversal CR embeddings of one CR manifold into another both of hypersurface type and nondegenerate. In chapter 2, in lower dimensions and when the target is the sphere, it is shown that at most two such embeddings exists up to holomorphic equivalence. Lifting such an embedding to an isometry between Fefferman bundles is discussed in chapter 3. In chapter 4 it is shown that transversal chain preserving embeddings between CR hypersurfaces must preserve CR structure. Finally in chapter 5 we discuss changes of the CR second fundamental form of a CR embedding by composition with automorphisms of the source and target