Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1101.53042
Ballmann, Werner
Lectures on Kähler manifolds. (English)
[B] ESI Lectures in Mathematics and Physics. Zürich: European Mathematical Society Publishing House. x, 172~p. EUR~38.00 (2006). ISBN 3-03719-025-6/pbk

This book is an introduction into the geometry of Kähler manifolds. Besides that, main aims of the author are cohomology of Kähler manifolds, formality of Kähler manifolds, Calabi Conjecture and some of its consequences, Gromov's Kähler hyperbolicity and Kodaira embedding theorem. Contents of this book; 1. Preliminaries (differential forms; Laplace operator; Hodge operator). 2. Complex manifolds. 3. Holomorphic vector bundles (Dolbeault Cohomology, Chern connection, line bundles). 4. Kähler manifolds. 5. Cohomology of Kähler manifolds (Lefschetz map and differentials, Lefschetz map and cohomology, the $dd_c$-lemma and formality, some vanishing theorems). 6. Ricci curvature and global structure (Ricci flat Kähler manifolds, nonnegative Ricci curvature, Ricci curvature and Laplace operator). 7. Calabi Conjecture. 8. Kähler hyperbolic spaces (Kähler hyperbolicity and Spectrum, non-vanishing of cohomology). 9. Kodaira embedding theorem and applications. Appendix A. Chern-Weil theory. Appendix B. Symmetric spaces (symmetric pairs, examples, Hermitian symmetric spaces). Appendix C. Remarks on differential operators (Dirac operators, $L^2$-de Rham cohomology, $L^2$-Dolbeault cohomology). This book contains many examples and exercises as well as a large list of literature consisting of 103 references.
[Nicolai K. Smolentsev (Kemerovo)]

MSC 2000:: *53C55 Complex differential geometry (global)
32Q15 Kähler manifolds
53-01 Textbooks (differential geometry)
53C15 Geometric structures on manifolds

Keywords: Kähler manifolds; cohomology of Kähler manifolds; Calabi conjecture; Kodaira embedding theorem; Kähler hyperbolicity; symmetric spaces

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]