Richard Schwartz

Abstract:   A hyperbolic structure on a manifold is a Riemannian metric of constant negative curvature. A spherical CR structure on a manifold is a system of coordinate charts into the 3-sphere such that the transition functions are restrictions of complex projective automorphisms which preserve the 3-sphere. I will explain my example of the first and still only known closed 3-manifold that admits both a hyperbolic and a spherical CR structure. The example is produced by considering deformations of reflection triangle groups into the isometry group of the complex hyperbolic plane, as I will explain in the talk.