Twistor theory for Riemannian symmetric spaces : with applications to harmonic maps of Riemann surfaces

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Twistor theory for Riemannian symmetric spaces : with applications to harmonic maps of Riemann surfaces

Francis E. Burstall, John H. Rawnsley

（Lecture notes in mathematics, 1424 . Scuola normale superiore, Pisa）

Springer-Verlag, c1990

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Includes bibliographical references and index

Description and Table of Contents

Description

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 Backlund 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.

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.

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