Twistor Theory for Riemannian Symmetric Spaces: With Applications to Harmonic Maps of Riemann Surfaces by Francis E. Burstall

Twistor Theory for Riemannian Symmetric Spaces: With Applications to Harmonic Maps of Riemann Surfaces

byFrancis E. Burstall, John H. Rawnsley

Paperback | May 22, 1990

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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.
Title:Twistor Theory for Riemannian Symmetric Spaces: With Applications to Harmonic Maps of Riemann Surfa...Format:PaperbackProduct dimensions:119 pages, 9.25 X 6.1 X 0 inShipping dimensions:119 pages, 9.25 X 6.1 X 0 inPublished:May 22, 1990Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540526021

ISBN - 13:9783540526025

Appropriate for ages: All ages

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Table of Contents

Homogeneous geometry.- Harmonic maps and twistor spaces.- Symmetric spaces.- Flag manifolds.- The twistor space of a Riemannian symmetric space.- Twistor lifts over Riemannian symmetric spaces.- Stable Harmonic 2-spheres.- Factorisation of harmonic spheres in Lie groups.