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Twistors, 4-symmetric spaces and integrable systems


Reference:

Burstall, F. E. and Khemar, I., 2009. Twistors, 4-symmetric spaces and integrable systems. Mathematische Annalen, 344 (2), pp. 451-461.

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Official URL:

http://dx.doi.org/10.1007/s00208-008-0313-5

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).

Details

Item Type Articles
CreatorsBurstall, F. E.and Khemar, I.
DOI10.1007/s00208-008-0313-5
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code25641

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