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An Introduction to CR Structures
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Mathematical Surveys and Monographs
1990; 237 pp; hardcover
Volume: 32
ISBN-10: 0-8218-1533-4
ISBN-13: 978-0-8218-1533-5
List Price: US$98 Member Price: US$78.40
Order Code: SURV/32

Parabolic Geometries I: Background and General Theory - Andreas Cap and Jan Slovak

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 self-contained 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 first-year graduate courses as background.

Reviews

"Recommended to specialists."

-- Zentralblatt MATH

• 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