**Mathematical Surveys and Monographs**

Volume: 140;
2007;
256 pp;
Hardcover

MSC: Primary 53; 32;

Print ISBN: 978-0-8218-4304-8

Product Code: SURV/140

List Price: $81.00

Individual Member Price: $64.80

**Electronic ISBN: 978-1-4704-1367-5
Product Code: SURV/140.E**

List Price: $81.00

Individual Member Price: $64.80

#### Supplemental Materials

# Foliations in Cauchy-Riemann Geometry

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*Elisabetta Barletta; Sorin Dragomir; Krishan L. Duggal*

The authors study the relationship between foliation theory and differential geometry and analysis on Cauchy–Riemann (CR) manifolds. The main objects of study are transversally and tangentially CR foliations, Levi foliations of CR manifolds, solutions of the Yang–Mills equations, tangentially Monge–Ampére foliations, the transverse Beltrami equations, and CR orbifolds. The novelty of the authors' approach consists in the overall use of the methods of foliation theory and choice of specific applications. Examples of such applications are Rea's holomorphic extension of Levi foliations, Stanton's holomorphic degeneracy, Boas and Straube's approximately commuting vector fields method for the study of global regularity of Neumann operators and Bergman projections in multi-dimensional complex analysis in several complex variables, as well as various applications to differential geometry. Many open problems proposed in the monograph may attract the mathematical community and lead to further applications of foliation theory in complex analysis and geometry of Cauchy–Riemann manifolds.

#### Table of Contents

# Table of Contents

## Foliations in Cauchy-Riemann Geometry

- Contents v6 free
- Preface vii8 free
- Chapter 1. Review of foliation theory 112 free
- Chapter 2. Foliated CR manifolds 1526
- Chapter 3. Levi foliations 4758
- Chapter 4. Levi foliations of CR submanifolds in CP[sup(N)] 7384
- Chapter 5. Tangentially CR foliations 8192
- Chapter 6. Transversally CR foliations 121132
- Chapter 7. G-Lie foliations 151162
- Chapter 8. Transverse Beltrami equations 163174
- Chapter 9. Review of orbifold theory 173184
- Chapter 10. Pseudo-differential operators on orbifolds 189200
- Chapter 11. Cauchy-Riemann Orbifolds 201212
- Appendix A. Holomorphic bisectional curvature 229240
- Appendix B. Partition of unity on orbifolds 231242
- Appendix C. Pseudo-differential operators on R[sup(n)] 237248
- Bibliography 243254
- Index 253264

#### Readership

Graduate students and research mathematicians interested in foliation theory with applications to differential geometry and complex analysis.