AMS Bookstore LOGO amslogo
Return to List  Item: 1 of 1   
Lectures on Kähler Manifolds
Werner Ballmann, Universität Bonn, Germany
A publication of the European Mathematical Society.
cover
ESI Lectures in Mathematics and Physics
2006; 182 pp; softcover
Volume: 2
ISBN-10: 3-03719-025-6
ISBN-13: 978-3-03719-025-8
List Price: US$44
Member Price: US$35.20
Order Code: EMSESILEC/2
[Add Item]

These notes are based on lectures the author gave at the University of Bonn and the Erwin Schrödinger Institute in Vienna. The aim is to give a thorough introduction to the theory of Kähler manifolds with special emphasis on the differential geometric side of Kähler geometry. The exposition starts with a short discussion of complex manifolds and holomorphic vector bundles and a detailed account of the basic differential geometric properties of Kähler manifolds. The more advanced topics are the cohomology of Kähler manifolds, Calabi conjecture, Gromov's Kähler hyperbolic spaces, and the Kodaira embedding theorem. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture. There are appendices on Chern-Weil theory, symmetric spaces, and \(L^2\)-cohomology.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and researchers in mathematics and theoretical physics.

Table of Contents

  • Preliminaries
  • Complex manifolds
  • Holomorphic vector bundles
  • Kähler manifolds
  • Cohomology of Kähler manifolds
  • Ricci curvature and global structure
  • Calabi conjecture
  • Kähler hyperbolic spaces
  • Kodaira embedding theorem
  • Appendix A. Chern-Weil theory
  • Appendix B. Symmetric spaces
  • Appendix C. Remarks on differential operators
  • Literature
  • Index
Powered by MathJax
Return to List  Item: 1 of 1   

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia