Buch, Englisch, 172 Seiten, PB, Format (B × H): 170 mm x 240 mm, Gewicht: 358 g
Buch, Englisch, 172 Seiten, PB, Format (B × H): 170 mm x 240 mm, Gewicht: 358 g
Reihe: ESI Lectures in Mathematics and Physics
ISBN: 978-3-03719-025-8
Verlag: EMS Press
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 L^2-cohomology.
Zielgruppe
Research mathematicians interested in differential geometry; graduate students. Readers are assumed to be familiar with basic concepts from differential geometry like vector bundles and connections, Riemannian and Hermitian metrics, curvature and holonomy. From analysis the basic facts of the theory of elliptic partial differential operators, in particular regularity and Hodge theory, are needed.
