Mathematical Surveys and Monographs 1990; 237 pp; hardcover Volume: 32 ISBN10: 0821815334 ISBN13: 9780821815335 List Price: US$103 Member Price: US$82.40 Order Code: SURV/32
 The geometry and analysis of CR manifolds is the subject of this expository work, which presents all the basic results on this topic, including results from the "folklore" of the subject. The book contains a careful exposition of seminal papers by Cartan and by Chern and Moser, and also includes chapters on the geometry of chains and circles and the existence of nonrealizable CR structures. With its detailed treatment of foundational papers, the book is especially useful in that it gathers in one volume many results that were scattered throughout the literature. Directed at mathematicians and physicists seeking to understand CR structures, this selfcontained exposition is also suitable as a text for a graduate course for students interested in several complex variables, differential geometry, or partial differential equations. A particular strength is an extensive chapter that prepares the reader for Cartan's approach to differential geometry. The book assumes only the usual firstyear graduate courses as background. Reviews "Recommended to specialists."  Zentralblatt MATH Table of Contents  CR Structures
 Some automorphism groups
 Formal theory of the normal form
 Geometric theory of the normal form
 Background for Cartan's work
 Cartan's construction
 Geometric consequences
 Chains
 Chains and circles in complex projective geometry
 Nonsolvability of the Lewy Operator
