Kähler-Einstein metrics and integral invariants
Author(s)
Bibliographic Information
Kähler-Einstein metrics and integral invariants
（Lecture notes in mathematics, 1314）
Springer-Verlag, c1988
- : gw
- : us
Available at / 75 libraries
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Library & Science Information Center, Osaka Prefecture University
: gwNDC8:410.8||||10009499133
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||13148807015S
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
: BerlinDC19:516.3/F9892070086106
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Note
Bibliography: p. [133]-139
Includes index
Description and Table of Contents
Description
These notes present very recent results on compact Kahler-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 Kahler-Einstein metric. Recent results concerning this character are collected here, dealing with its origin, generalizations, sufficiency for the existence of a Kahler-Einstein metric and lifting to a group character. Other related topics such as extremal Kahler metrics studied by Calabi and others and the existence results of Tian and Yau are also reviewed. As the rudiments of Kahlerian 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.
Table of Contents
Preliminaries.- Kahler-Einstein metrics and extremal Kahler metrics.- The character f and its generalization to Kahlerian 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.
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