TY - BOOK
AU - Dragomir,Sorin
AU - Tomassini,Giuseppe
ED - SpringerLink (Online service)
TI - Differential Geometry and Analysis on CR Manifolds
T2 - Progress in Mathematics
SN - 9780817644833
AV - QA641-670
U1 - 516.36 23
PY - 2006///
CY - Boston, MA
PB - Birkhäuser Boston
KW - Mathematics
KW - Mathematical analysis
KW - Analysis (Mathematics)
KW - Global analysis (Mathematics)
KW - Manifolds (Mathematics)
KW - Partial differential equations
KW - Functions of complex variables
KW - Differential geometry
KW - Differential Geometry
KW - Global Analysis and Analysis on Manifolds
KW - Partial Differential Equations
KW - Several Complex Variables and Analytic Spaces
KW - Analysis
N1 - 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
N2 - 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
UR - http://dx.doi.org/10.1007/0-8176-4483-0
ER -