Overview

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.

Full Product Details

Author:   Gang Tian ,  M. Akveld
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2000 ed.
Dimensions:   Width: 17.80cm , Height: 0.50cm , Length: 25.40cm
Weight:   0.460kg
ISBN:  

9783764361945

ISBN 10:   3764361948
Pages:   101
Publication Date:   01 August 2000
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

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.

Reviews

This little monograph offers an essentially self-contained introduction to the theory of canonical KAhler metrics on complex manifolds. a ]The author presents some advanced topics which are hard [to] find elsewherea ] This graduate course on KAhler-Einstein metrics can be recommended to all those interested in recent developments within complex differential geometry. <p>--Publicationes Mathematicae <p> This monograph includes an essentially self-contained introduction to the theory of canonical KAhler metrics on complex manifolds. <p>--Zentralblatt Math

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions