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Kähler-Einstein metrics and integral invariants / Akito Futaki.

By: Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1314.Publication details: Berlin ; New York : Springer-Verlag, ©1988.Description: 1 online resource (iv, 139 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540391722
  • 354039172X
Subject(s): Additional physical formats: Print version:: Kähler-Einstein metrics and integral invariants.DDC classification:
  • 510 s 516.3/62 19
LOC classification:
  • QA3 .L28 no. 1314 QA614
Other classification:
  • 31.52
Online resources:
Contents:
Introduction -- Preliminaries -- Khler-Einstein Metrics and Extremal Khler Metrics -- The Character f and its Generalization to Khlerian 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 -- References -- Index.
Summary: These notes present very recent results on compact Khler-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 Khler-Einstein metric. Recent results concerning this character are collected here, dealing with its origin, generalizations, sufficiency for the existence of a Khler-Einstein metric and lifting to a group character. Other related topics such as extremal Khler metrics studied by Calabi and others and the existence results of Tian and Yau are also reviewed. As the rudiments of Khlerian 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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Includes bibliographical references (pages 133-139) and index.

Introduction -- Preliminaries -- Khler-Einstein Metrics and Extremal Khler Metrics -- The Character f and its Generalization to Khlerian 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 -- References -- Index.

These notes present very recent results on compact Khler-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 Khler-Einstein metric. Recent results concerning this character are collected here, dealing with its origin, generalizations, sufficiency for the existence of a Khler-Einstein metric and lifting to a group character. Other related topics such as extremal Khler metrics studied by Calabi and others and the existence results of Tian and Yau are also reviewed. As the rudiments of Khlerian 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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