Kähler-Einstein Metrics and Integral Invariants

by Akito Futaki

Overview

These notes present very recent results on compact Kähler-Einstein manifolds of positive scalar curvature. A central role is played here by a Lie algebra character of the complex Lie algebra consisting of all holomorphic vector fields, which can be intrinsically defined on any compact complex manifold and becomes an obstruction to the existence of a Kähler-Einstein metric. Recent results concerning this character are collected here, dealing with its origin, generalizations, sufficiency for the existence of a Kähler-Einstein metric and lifting to a group character. Other related topics such as extremal Kähler metrics studied by Calabi and others and the existence results of Tian and Yau are also reviewed. As the rudiments of Kählerian geometry and Chern-Simons theory are presented in full detail, these notes are accessible to graduate students as well as to specialists of the subject.

Product Details

ISBN-13:	9783540192503
Publisher:	Springer Berlin Heidelberg
Publication date:	06/13/1988
Series:	Lecture Notes in Mathematics , #1314
Edition description:	1988
Pages:	140
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Preliminaries.- Kähler-Einstein metrics and extremal Kähler metrics.- The character f and its generalization to Kählerian invariants.- The character f as an obstruction.- The character f as a classical invariant.- Lifting f to a group character.- The character f as a moment map.- Aubin's approach and related results.