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

Twistor Theory for Riemannian Symmetric Spaces

With Applications to Harmonic Maps of Riemann Surfaces

Paperback

Published: 22nd May 1990
Ships: 5 to 9 business days
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$57.18

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.

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.

ISBN: 9783540526025
ISBN-10: 3540526021
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 110
Published: 22nd May 1990
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 0.66
Weight (kg): 0.19