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＜E-Book＞
Canonical Metrics in Kähler Geometry / by Gang Tian
(Lectures in Mathematics. ETH Zürich)

Edition	1st ed. 2000.
Publisher	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
Year	2000
Size	VII, 101 p : online resource
Authors	*Tian, Gang author SpringerLink (Online service)
Subjects	LCSH:Geometry, Differential LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Mathematical physics FREE:Differential Geometry FREE:Global Analysis and Analysis on Manifolds FREE:Mathematical Methods in Physics
Notes	1 Introduction to Kähler manifolds -- 1.1 Kähler metrics -- 1.2 Curvature of Kähler metrics -- 2 Extremal Kähler metrics -- 2.1 The space of Kähler metrics -- 2.2 A brief review of Chern classes -- 2.3 Uniformization of Kähler-Einstein manifolds -- 3 Calabi-Futaki invariants -- 3.1 Definition of Calabi-Futaki invariants -- 3.2 Localization formula for Calabi-Futaki invariants -- 4 Scalar curvature as a moment map -- 5 Kähler-Einstein metrics with non-positive scalar curvature -- 5.1 The Calabi-Yau Theorem -- 5.2 Kähler-Einstein metrics for manifolds with c1(M) < 0 -- 6 Kähler-Einstein metrics with positive scalar curvature -- 6.1 A variational approach -- 6.2 Existence of Kähler-Einstein metrics -- 6.3 Examples -- 7 Applications and generalizations -- 7.1 A manifold without Kähler-Einstein metric -- 7.2 K-energy and metrics of constant scalar curvature -- 7.3 Relation to stability HTTP:URL=https://doi.org/10.1007/978-3-0348-8389-4

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