Differential Geometry and Analysis on CR Manifolds
Dragomir, Sorin.
creator
author.
Tomassini, Giuseppe.
author.
SpringerLink (Online service)
text
xxu
2006
monographic
eng
access
XVI, 488 p. online resource.
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.
CR Manifolds -- The Fefferman Metric -- The CR Yamabe Problem -- Pseudoharmonic Maps -- Pseudo-Einsteinian Manifolds -- Pseudo-Hermitian Immersions -- Quasiconformal Mappings -- Yang-Mills Fields on CR Manifolds -- Spectral Geometry.
by Sorin Dragomir, Giuseppe Tomassini.
Mathematics
Mathematical analysis
Analysis (Mathematics)
Global analysis (Mathematics)
Manifolds (Mathematics)
Partial differential equations
Functions of complex variables
Differential geometry
Mathematics
Differential Geometry
Global Analysis and Analysis on Manifolds
Partial Differential Equations
Several Complex Variables and Analytic Spaces
Analysis
QA641-670
516.36
Springer eBooks
Progress in Mathematics ; 246
9780817644833
http://dx.doi.org/10.1007/0-8176-4483-0
http://dx.doi.org/10.1007/0-8176-4483-0
100301
20180115171433.0
978-0-8176-4483-3