Canonical metrics in Kähler geometry
著者
書誌事項
Canonical metrics in Kähler geometry
（Lectures in mathematics ETH Zürich）
Birkhäuser, c2000
- : Basel
- : Boston
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注記
Includes bibliographical references ( p. [99]-100) and index
内容説明・目次
内容説明
There has been fundamental progress in complex differential geometry in the last two decades. For one, The uniformization theory of canonical Kahler metrics has been established in higher dimensions, and many applications have been found, including the use of Calabi-Yau spaces in superstring theory. This monograph gives an introduction to the theory of canonical Kahler metrics on complex manifolds. It also presents some advanced topics not easily found elsewhere.
目次
1 Introduction to Kahler manifolds.- 1.1 Kahler metrics.- 1.2 Curvature of Kahler metrics.- 2 Extremal Kahler metrics.- 2.1 The space of Kahler metrics.- 2.2 A brief review of Chern classes.- 2.3 Uniformization of Kahler-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 Kahler-Einstein metrics with non-positive scalar curvature.- 5.1 The Calabi-Yau Theorem.- 5.2 Kahler-Einstein metrics for manifolds with c1(M) < 0.- 6 Kahler-Einstein metrics with positive scalar curvature.- 6.1 A variational approach.- 6.2 Existence of Kahler-Einstein metrics.- 6.3 Examples.- 7 Applications and generalizations.- 7.1 A manifold without Kahler-Einstein metric.- 7.2 K-energy and metrics of constant scalar curvature.- 7.3 Relation to stability.
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