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Kähler-Einstein Metrics and Integral Invariants

  • Book
  • © 1988

Overview

Authors:
  1. Akito Futaki
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1314)

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About this book

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.

Keywords

Table of contents (9 chapters)

  1. Front Matter

    Pages I-IV
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  2. Introduction

    • Akito Futaki
    Pages 1-6

  3. Preliminaries

    • Akito Futaki
    Pages 7-30

  4. Kähler-Einstein metrics and extremal Kähler metrics

    • Akito Futaki
    Pages 31-45

  5. The character f and its generalization to Kählerian invariants

    • Akito Futaki
    Pages 46-55

  6. The character f as an obstruction

    • Akito Futaki
    Pages 56-67

  7. The character f as a classical invariant

    • Akito Futaki
    Pages 68-86

  8. Lifting f to a group character

    • Akito Futaki
    Pages 87-98

  9. The character f as a moment map

    • Akito Futaki
    Pages 99-112

  10. Aubin's approach and related results

    • Akito Futaki
    Pages 113-132

  11. Back Matter

    Pages 133-140
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Bibliographic Information

  • Book Title: Kähler-Einstein Metrics and Integral Invariants

  • Authors: Akito Futaki

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0078084

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1988

  • Softcover ISBN: 978-3-540-19250-3Published: 11 May 1988

  • eBook ISBN: 978-3-540-39172-2Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IV, 140

  • Topics: Differential Geometry, Algebraic Geometry

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