Canonical Metrics in Kähler Geometry
Published on 1. August 2000
Book
Paperback/Softback
VII, 101 pages
978-3-7643-6194-5 (ISBN)
Description
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.
Reviews / Votes
"This little monograph offers an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds. .The author presents some advanced topics which are hard [to] find elsewhere. This graduate course on Kähler-Einstein metrics can be recommended to all those interested in recent developments within complex differential geometry."
--Publicationes Mathematicae
"This monograph includes an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds."
--Zentralblatt Math
More details
Series
Edition
2000 ed.
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
VII, 101 p.
Dimensions
Height: 254 mm
Width: 178 mm
Thickness: 7 mm
Weight
228 gr
ISBN-13
978-3-7643-6194-5 (9783764361945)
DOI
10.1007/978-3-0348-8389-4
Schweitzer Classification
Persons
Content
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.