02313nam 22004335a 450 991015193740332120091109150325.03-03719-525-810.4171/025(CKB)3710000000953801(CH-001817-3)42-091109(PPN)178155128(EXLCZ)99371000000095380120091109j20060710 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierLectures on Kähler Manifolds[electronic resource] /Werner BallmannZuerich, Switzerland European Mathematical Society Publishing House20061 online resource (182 pages)ESI Lectures in Mathematics and Physics (ESI)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.Differential & Riemannian geometrybicsscDifferential geometrymscSeveral complex variables and analytic spacesmscGlobal analysis, analysis on manifoldsmscDifferential & Riemannian geometryDifferential geometrySeveral complex variables and analytic spacesGlobal analysis, analysis on manifolds53-xx32-xx58-xxmscBallmann Werner471658ch0018173BOOK9910151937403321Lectures on Kähler manifolds229437UNINA