**Mathematical Surveys and Monographs**

Volume: 32;
1990;
237 pp;
Hardcover

MSC: Primary 32;
Secondary 53

Print ISBN: 978-0-8218-1533-5

Product Code: SURV/32

List Price: $103.00

Individual Member Price: $82.40

**Electronic ISBN: 978-1-4704-1259-3
Product Code: SURV/32.E**

List Price: $103.00

Individual Member Price: $82.40

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# An Introduction to CR Structures

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*Howard J. Jacobowitz*

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 & Endorsements

Recommended to specialists.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## An Introduction to CR Structures

- Contents vii8 free
- Preface ix10 free
- Chapter 1. CR Structures 112 free
- Chapter 2. Some Automorphism Groups 3546
- Chapter 3. Formal Theory of the Normal Form 5768
- Chapter 4. Geometric Theory of the Normal Form 6778
- Chapter 5. Background for Cartan's Work 89100
- Chapter 6. Cartan's Construction 117128
- Chapter 7. Geometric Consequences 147158
- Chapter 8. Chains 157168
- Chapter 9. Chains and Circles in Complex Projective Geometry 189200
- Chapter 10. Nonsolvability of the Lewy Operator 209220
- Notes 227238
- References 233244
- Index 237248 free