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Transformation Groups in Differential Geometry

  • Shoshichi Kobayashi

Part of the Classics in Mathematics book series (volume 70)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Shoshichi Kobayashi
    Pages 1-38
  3. Shoshichi Kobayashi
    Pages 39-76
  4. Shoshichi Kobayashi
    Pages 77-121
  5. Shoshichi Kobayashi
    Pages 122-149
  6. Back Matter
    Pages 150-182

About this book

Introduction

Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc­ tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo­ metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec­ tures I gave in Tokyo and Berkeley in 1965.

Keywords

Lie group automorphism differential geometry transformation group

Authors and affiliations

  • Shoshichi Kobayashi
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-61981-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58659-3
  • Online ISBN 978-3-642-61981-6
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site