ESI Lectures in Mathematics and Physics 2006; 182 pp; softcover Volume: 2 ISBN10: 3037190256 ISBN13: 9783037190258 List Price: US$44 Member Price: US$35.20 Order Code: EMSESILEC/2
 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 ChernWeil 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. ChernWeil theory
 Appendix B. Symmetric spaces
 Appendix C. Remarks on differential operators
 Literature
 Index
