Twistor Theory for Riemannian Symmetric Spaces

With Applications to Harmonic Maps of Riemann Surfaces

Francis E. Burstall, John H. Rawnsley (Autoren)

Buch | Softcover

110 Seiten

1990 | 1990
Springer Berlin (Verlag)
978-3-540-52602-5 (ISBN)

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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.

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.

Erscheint lt. Verlag	22.5.1990
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	110 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Differentialgeometrie • Differential Geometry • Differenzialgeometrie • harmonic maps • manifold • minimal surface • minimal surfaces • Riemannian symmetric spaces • Riemannsche Flächen • Riemannsche Räume • Twistor theory
ISBN-10	3-540-52602-1 / 3540526021
ISBN-13	978-3-540-52602-5 / 9783540526025
Zustand	Neuware