Ballmann, Werner,
Lectures on Kähler Manifolds [electronic resource] / Werner Ballmann - Zuerich, Switzerland : European Mathematical Society Publishing House, 2006 - 1 online resource (182 pages) - ESI Lectures in Mathematics and Physics (ESI) .
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
These notes are based on lectures the author held 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 L2-cohomology.
9783037195253
10.4171/025 doi
Differential & Riemannian geometry
Differential geometry
Several complex variables and analytic spaces
Global analysis, analysis on manifolds
Lectures on Kähler Manifolds [electronic resource] / Werner Ballmann - Zuerich, Switzerland : European Mathematical Society Publishing House, 2006 - 1 online resource (182 pages) - ESI Lectures in Mathematics and Physics (ESI) .
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
These notes are based on lectures the author held 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 L2-cohomology.
9783037195253
10.4171/025 doi
Differential & Riemannian geometry
Differential geometry
Several complex variables and analytic spaces
Global analysis, analysis on manifolds