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Lectures on Kähler Manifolds
ESI Lectures in Mathematics and Physics

Werner Ballmann (University of Bonn, Germany)

Lectures on Kähler Manifolds

ISBN print 978-3-03719-025-8, ISBN online 978-3-03719-525-3
DOI 10.4171/025
July 2006, 182 pages, softcover, 17 x 24 cm.
38.00 Euro

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.

Further Information

Review in Zentralblatt MATH 1101.53042

Review in MR 2243012 (2007e:32026)