Differential Geometry and Analysis on CR Manifolds [electronic resource] /
Dragomir, Sorin.author.
Tomassini, Giuseppe.author.
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 achievements 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.
Description based upon print version of record.
Includes bibliographical references (p. [463]-482) and index.
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.
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 achievements 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.
Differential geometry.
Global analysis (Mathematics).
Manifolds (Mathematics).
Partial differential equations.
Functions of complex variables.
Mathematical analysis.
Analysis (Mathematics).
Differential Geometry.
Global Analysis and Analysis on Manifolds.
Partial Differential Equations.
Several Complex Variables and Analytic Spaces.
Analysis.