Twistor Theory for Riemannian Symmetric Spaces

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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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.

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

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

  Francis E. Burstall

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

  John H. Rawnsley

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