Geometry of embedded CR manifolds

Abstract

The reader is introduced to the geometry of CR manifolds, which are real submanifolds of complex space with a complex structure on a subbundle of its tangent bundle. Explicit formulas for the geometrical aspects of CR(1,1) manifolds are given, including formulas for the Reeb vector field, the Tanaka-Webster connection and the pseudo-holomorphic sectional curvature.