Differential Geometry and Analysis on CR Manifolds

Sorin Dragomir, Giuseppe Tomassini - Collection Progress in Mathematics

504 pages, parution le 15/01/2006

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Résumé

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.

Written for: Researchers and graduate students in differential geometry, complex analysis, and PDEs

Sommaire

CR Manifolds
The Fefferman Metric
The CR Yamabe Problem
Pseudoharmonic Maps
Pseudo-Einstein Manifolds
Pseudohermitian Immersions
Quasiconformal Mappings
Yang-Mills Fields on CR Manifolds
Spectral Geometry
Appendix

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Sorin Dragomir, Giuseppe Tomassini
Collection	Progress in Mathematics
Parution	15/01/2006
Nb. de pages	504
Format	16 x 24
Couverture	Relié
Poids	825g
Intérieur	Noir et Blanc
EAN13	9780817643881
ISBN13	978-0-8176-4388-1