Lectures on Kähler Manifolds

Front Cover
European Mathematical Society, 2006 - Mathematics - 172 pages
These notes are based on lectures the author gave at the University of Bonn and the Erwin Schrodinger Institute in Vienna. The aim is to give a thorough introduction to the theory of Kahler manifolds with special emphasis on the differential geometric side of Kahler 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 Kahler manifolds. The more advanced topics are the cohomology of Kahler manifolds, Calabi conjecture, Gromov's Kahler 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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Contents
1
Complex Manifolds II
11
JXJY XY
17
Holomorphic Vector Bundles
29
Kahler Manifolds
41
Then the associated differential twoform co defined
51
Cohomology of Kahler Manifolds
60
Ricci Curvature and Global Structure
80
Kahler Hyperbolic Spaces
103
Kodaira Embedding Theorem
114
Appendix A ChernWeil Theory
121
Appendix B Symmetric Spaces
134
Remarks on Differential Operators
157
Literature
165
Index
171
Copyright

Calabi Conjecture
86

Common terms and phrases

Bibliographic information