ENGLISH

Foliations in Cauchy-Riemann Geometry (Mathematical Surveys and Monographs)

By Sorin Dragomir , Elisabetta Barletta , Krishan L. Duggal

Book information

Publisher
American Mathematical Society
Year
2007
ISBN
0821843044, 9780821843048
LCC
QA613.62 .B37 2007
Open Library ID
OL11420279M
Language
english
Format
PDF
Filesize
7 MB (7027743 bytes)
Pages
270\270
Time added
2010-02-18 13:16:04

Description

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-AmpГѓВ©re 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.

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