© 2006

Differential Geometry and Analysis on CR Manifolds


Part of the Progress in Mathematics book series (PM, volume 246)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Pages 1-108
  3. Pages 109-156
  4. Pages 157-209
  5. Pages 211-274
  6. Pages 377-406
  7. Pages 423-443
  8. Back Matter
    Pages 445-487

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.


CR manifold Complex analysis calculus differential equation differential geometry manifold partial differential equation

Authors and affiliations

  1. 1.Dipartimento de Matematica, Contrada Macchia RomanaUniversità degli Studi della BasilicataPotenzaItaly
  2. 2.Classe di ScienzeScuola Normale SuperiorePisaItaly

Bibliographic information


In fact, it will be invaluable for people working on the differential geometry of CR manifolds. –Thomas Garity, MathSciNet