Foliations in Cauchy-Riemann geometry / Elisabetta Barletta, Sorin Dragomir, Krishan L. Duggal.

Format:

Book

Author/Creator:

Barletta, Elisabetta, 1957- author.

Dragomir, Sorin, 1955- author.

Duggal, Krishan L., 1929- author.

Series:

Mathematical surveys and monographs ; volume 140.

Mathematical surveys and monographs, 0076-5376 ; volume 140

Language:

English

Subjects (All):

Foliations (Mathematics).

Cauchy-Riemann equations.

Physical Description:

1 online resource (270 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2007]

Language Note:

English

Summary:

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-Ampere 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

Contents:

""Contents""; ""Preface""; ""Chapter 1. Review of foliation theory""; ""1.1. Basic notions""; ""1.2. Transverse geometry""; ""Chapter 2. Foliated CR manifolds""; ""2.1. The normal bundle""; ""2.2. Foliations of CR manifolds and the Fefferman metric""; ""2.3. Foliated Lorentz manifolds""; ""2.4. The second fundamental form""; ""2.5. The characteristic form""; ""Chapter 3. Levi foliations""; ""3.1. Existence of Levi foliations""; ""3.2. Holomorphic extension of Levi foliations""; ""3.3. Pluriharmonic defining functions""; ""3.4. Holomorphic degeneracy""; ""3.5. Twistor CR manifolds""

""6.1. Transversally CR foliations""""6.2. CR foliations built by suspension""; ""6.3. Transverse pseudohermitian geometry""; ""6.4. Degenerate CR manifolds""; ""6.5. The transverse Cauchy-Riemann complex""; ""6.6. Canonical transverse connections""; ""6.7. The embedding problem""; ""Chapter 7. G-Lie foliations""; ""7.1. G-Lie foliations and transverse CR structures""; ""7.2. Transverse f-structures""; ""Chapter 8. Transverse Beltrami equations""; ""8.1. Automorphisms of the transverse contact structure""; ""8.2. K-quasiconformal automorphisms""; ""Chapter 9. Review of orbifold theory""

""9.1. Defining families""""9.2. The local structure of S""; ""9.3. The monomorphism . . .""; ""9.4. The singular locus""; ""9.5. Vector bundles over orbifolds""; ""9.6. Transition functions""; ""9.7. Compact Hausdorff foliations""; ""Chapter 10. Pseudo-differential operators on orbifolds""; ""10.1. The Girbau-Nicolau condition""; ""10.2. Composition of pseudo-differential operators""; ""10.3. Elliptic operators on orbifolds""; ""Chapter 11. Cauchy-Riemann Orbifolds""; ""11.1. Parabolic geodesics""; ""11.2. Complex orbifolds""; ""11.3. Real hypersurfaces""; ""11.4. CR orbifolds""

""11.5. A parametrix for . . .""""Appendix A. Holomorphic bisectional curvature""; ""Appendix B. Partition of unity on orbifolds""; ""Appendix C. Pseudo-differential operators on R[sup(n)]""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""V""; ""W""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 243-252) and index.

Description based on print version record.

ISBN:

1-4704-1367-1