Authors:
- Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form
- Explains how certain results from analysis are employed in CR geometry
- Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook
- Provides unproved statements and comments inspiring further study
Part of the book series: Progress in Mathematics (PM, volume 246)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
About this book
The study of CR manifolds lies at the intersection of three main mathematical disciplines: partial differential equations, complex analysis in several complex variables, and differential geometry. While the PDE and complex analytic aspects have been intensely studied in the last fifty years, much effort has recently been made to understand the differential geometric side of the subject.
This monograph provides a unified presentation of several differential geometric aspects in the theory of CR manifolds and tangential Cauchy–Riemann equations. It presents the major differential geometric acheivements in the theory of CR manifolds, such as the Tanaka–Webster connection, Fefferman's metric, pseudo-Einstein structures and the Lee conjecture, CR immersions, subelliptic harmonic maps as a local manifestation of pseudoharmonic maps from a CR manifold, Yang–Mills fields on CR manifolds, to name a few. It also aims at explaining how certain results from analysis are employed in CR geometry.
Motivated by clear exposition, many examples, explicitly worked-out geometric results, and stimulating unproved statements and comments referring to the most recent aspects of the theory, this monograph is suitable for researchers and graduate students in differential geometry, complex analysis, and PDEs.
Reviews
In fact, it will be invaluable for people working on the differential geometry of CR manifolds. –Thomas Garity, MathSciNet
Authors and Affiliations
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Dipartimento de Matematica, Contrada Macchia Romana, Università degli Studi della Basilicata, Potenza, Italy
Sorin Dragomir
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Classe di Scienze, Scuola Normale Superiore, Pisa, Italy
Giuseppe Tomassini
Bibliographic Information
Book Title: Differential Geometry and Analysis on CR Manifolds
Authors: Sorin Dragomir, Giuseppe Tomassini
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/0-8176-4483-0
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2006
Hardcover ISBN: 978-0-8176-4388-1
eBook ISBN: 978-0-8176-4483-3
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XVI, 488
Topics: Differential Geometry, Global Analysis and Analysis on Manifolds, Partial Differential Equations, Several Complex Variables and Analytic Spaces, Analysis