El. knyga: Differential Geometry and Analysis on CR Manifolds

This monograph provides a unified presentation of several differential geometric aspects in the theory of CR manifolds and tangential Cauchy-Riemann equations. It presents the major differential geometric acheivements in the theory of CR manifolds, such as the Tanaka-Webster connection, Fefferman's metric, pseudo-Einstein structures and the Lee conjecture, CR immersions, subelliptic harmonic maps as a local manifestation of pseudoharmonic maps from a CR manifold, Yang-Mills fields on CR manifolds, to name a few. It also aims at explaining how certain results from analysis are employed in CR geometry.

Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form

Explains how certain results from analysis are employed in CR geometry

Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook

Provides unproved statements and comments inspiring further study

Recent years have seen a concerted effort to understand the differential geometric side of the study of CR manifolds. This monograph provides a unified presentation of several differential geometric aspects in the theory of CR manifolds and tangential Cauchy-Riemann equations. It contains many examples, explicitly worked-out geometric results, and stimulating unproved statements and comments referring to the most recent aspects of the theory.