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Twistor Theory for Riemannian Symmetric Spaces

With Applications to Harmonic Maps of Riemann Surfaces

  • Conference proceedings
  • © 1990

Overview

Authors:
  1. Francis E. Burstall

    1. School of Mathematical Sciences, University of Bath, Bath, Great Britain

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  2. John H. Rawnsley

    1. Mathematics Institute, University of Warwick, Coventry, Great Britain

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

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Table of contents (9 papers)

  1. Front Matter

    Pages i-iii
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  2. Introduction

    • Francis E. Burstall, John H. Rawnsley
    Pages 1-5

  3. Homogeneous geometry

    • Francis E. Burstall, John H. Rawnsley
    Pages 6-14

  4. Harmonic maps and twistor spaces

    • Francis E. Burstall, John H. Rawnsley
    Pages 15-21

  5. Symmetric spaces

    • Francis E. Burstall, John H. Rawnsley
    Pages 22-38

  6. Flag manifolds

    • Francis E. Burstall, John H. Rawnsley
    Pages 39-62

  7. The twistor space of a Riemannian symmetric space

    • Francis E. Burstall, John H. Rawnsley
    Pages 63-70

  8. Twistor lifts over Riemannian symmetric spaces

    • Francis E. Burstall, John H. Rawnsley
    Pages 71-80

  9. Stable Harmonic 2-spheres

    • Francis E. Burstall, John H. Rawnsley
    Pages 81-89

  10. Factorisation of harmonic spheres in Lie groups

    • Francis E. Burstall, John H. Rawnsley
    Pages 90-105

  11. Back Matter

    Pages 106-116
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Keywords

About this book

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.

Authors and Affiliations

  • School of Mathematical Sciences, University of Bath, Bath, Great Britain

    Francis E. Burstall

  • Mathematics Institute, University of Warwick, Coventry, Great Britain

    John H. Rawnsley

Bibliographic Information

  • Book Title: Twistor Theory for Riemannian Symmetric Spaces

  • Book Subtitle: With Applications to Harmonic Maps of Riemann Surfaces

  • Authors: Francis E. Burstall, John H. Rawnsley

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0095561

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1990

  • Softcover ISBN: 978-3-540-52602-5Published: 22 May 1990

  • eBook ISBN: 978-3-540-47052-6Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: 110

  • Topics: Differential Geometry, Topological Groups, Lie Groups, Fourier Analysis

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