This book, Differential Geometry: Advanced Topics in CR and Pseudohermitian Geometry (Book I-D), is the fourth in a series of four books presenting a choice of advanced topics in Cauchy–Riemann (CR) and pseudohermitian geometry, such as Fefferman metrics, global behavior of tangential CR equations, Rossi spheres, the CR Yamabe problem on a CR manifold-with-boundary, Jacobi fields of the Tanaka–Webster connection, the theory of CR immersions versus Lorentzian geometry. The book also discusses boundary values of proper holomorphic maps of balls, Beltrami equations on Rossi spheres within the Koranyi–Reimann theory of quasiconformal mappings of CR manifolds, and pseudohermitian analogs to the Gauss–Ricci–Codazzi equations in the study of CR immersions between strictly pseudoconvex CR manifolds. The other three books of the series are:

         Differential Geometry: Manifolds, Bundles, Characteristic Classes (Book I-A)

         Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B)

         Differential Geometry: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book...