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Twistor Theory for Riemannian Symmetric Spaces

With Applications to Harmonic Maps of Riemann Surfaces

  • Francis E. Burstall
  • John H. Rawnsley

Part of the Lecture Notes in Mathematics book series (LNM, volume 1424)

Table of contents

  1. Front Matter
    Pages i-iii
  2. Francis E. Burstall, John H. Rawnsley
    Pages 1-5
  3. Francis E. Burstall, John H. Rawnsley
    Pages 6-14
  4. Francis E. Burstall, John H. Rawnsley
    Pages 15-21
  5. Francis E. Burstall, John H. Rawnsley
    Pages 22-38
  6. Francis E. Burstall, John H. Rawnsley
    Pages 39-62
  7. Francis E. Burstall, John H. Rawnsley
    Pages 63-70
  8. Francis E. Burstall, John H. Rawnsley
    Pages 71-80
  9. Francis E. Burstall, John H. Rawnsley
    Pages 81-89
  10. Francis E. Burstall, John H. Rawnsley
    Pages 90-105
  11. Back Matter
    Pages 106-116

About these proceedings

Introduction

In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces. In particular, flag manifolds are shown to arise as twistor spaces of Riemannian symmetric spaces. Applications of this theory include a complete classification of stable harmonic 2-spheres in Riemannian symmetric spaces and a Bäcklund transform for harmonic 2-spheres in Lie groups which, in many cases, provides a factorisation theorem for such spheres as well as gap phenomena. The main methods used are those of homogeneous geometry and Lie theory together with some algebraic geometry of Riemann surfaces. The work addresses differential geometers, especially those with interests in minimal surfaces and homogeneous manifolds.

Keywords

Differential geometry Minimal surface Minimal surfaces Riemannian symmetric spaces Twistor theory harmonic maps manifold

Authors and affiliations

  • Francis E. Burstall
    • 1
  • John H. Rawnsley
    • 2
  1. 1.School of Mathematical SciencesUniversity of BathBathGreat Britain
  2. 2.Mathematics InstituteUniversity of WarwickCoventryGreat Britain

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0095561
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-52602-5
  • Online ISBN 978-3-540-47052-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site