ENGLISH

Kähler-Einstein Metrics and Integral Invariants

By Akito Futaki

Book information

Publisher
Springer
Year
1988
ISBN
0387192506, 9780387192505
LCC
QA3 .L28 no. 1314,QA614 .L28 no. 1314
Language
english
Format
PDF
Filesize
3 MB (3275055 bytes)
Series
Lecture Notes in Mathematics 1314
Pages
139\146
Time added
2012-03-09 12:00:00

Description

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.

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