Twistor Theory for Riemannian Synmetric Spaces with Applications to Harmonic Maps of Riemann Surfaces
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published: May 1990
Format: Paperback
Number of pages: 115
ISBN-13: 9783540526025
Subjects: Differential & Riemannian geometry
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 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.