Twistors, 4-symmetric spaces and integrable systems

Francis E Burstall, Idrisse Khemar

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

An order four automorphism of a Lie algebra gives rise to an integrable system introduced by Terng. We show that solutions of this system may be identified with certain vertically harmonic twistor lifts of conformal maps of surfaces in a Riemannian symmetric space. As applications, we find that surfaces with holomorphic mean curvature in 4-dimensional real or complex space forms constitute an integrable system as do Hamiltonian stationary Lagrangian surfaces in 4-dimensional Hermitian symmetric spaces (this last providing a conceptual explanation of a result of Hélein-Romon).
Original languageEnglish
Pages (from-to)451-461
Number of pages11
JournalMathematische Annalen
Volume344
Issue number2
Early online date4 Dec 2008
DOIs
Publication statusPublished - Jun 2009

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Twistors
Integrable Systems
Symmetric Spaces
Lagrangian Surfaces
Hermitian Symmetric Spaces
Complex Space Form
Riemannian Symmetric Space
Conformal Map
Mean Curvature
Automorphism
Lie Algebra
Harmonic

Cite this

Twistors, 4-symmetric spaces and integrable systems. / Burstall, Francis E; Khemar, Idrisse.

In: Mathematische Annalen, Vol. 344, No. 2, 06.2009, p. 451-461.

Research output: Contribution to journalArticle

Burstall, Francis E ; Khemar, Idrisse. / Twistors, 4-symmetric spaces and integrable systems. In: Mathematische Annalen. 2009 ; Vol. 344, No. 2. pp. 451-461.
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