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Kähler-Einstein Metrics and Integral Invariants

  • Authors
  • Akito Futaki

Part of the Lecture Notes in Mathematics book series (LNM, volume 1314)

Table of contents

  1. Front Matter
    Pages I-IV
  2. Akito Futaki
    Pages 1-6
  3. Akito Futaki
    Pages 7-30
  4. Akito Futaki
    Pages 56-67
  5. Akito Futaki
    Pages 68-86
  6. Akito Futaki
    Pages 87-98
  7. Akito Futaki
    Pages 99-112
  8. Akito Futaki
    Pages 113-132
  9. Back Matter
    Pages 133-140

About this book

Introduction

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

Grad Invariant Lie Microsoft Access Simon Vector field algebra boundary element method curvature eXist geometry group lie algebra manifold metrics

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0078084
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-19250-3
  • Online ISBN 978-3-540-39172-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site