Twistors, 4-symmetric spaces and integrable systems

Details Twistors, 4-symmetric spaces and integrable systems Twistors, 4-symmetric spaces and integrable systems

2008-04-28

arxiv.org/abs/0804.4235v2

Math. Ann. 344 (2009) 451-461

Mathematics

Differential Geometry

9 pages. v2: corrected typo in metadata

Scientific paper

10.1007/s00208-008-0313-5

An order four automorphism of a Lie algebra gives rise to an integrable system discussed 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. Specialising to 4-dimensional target, we find that surfaces with holomorphic mean curvature in 4-dimensional spaces with constant sectional or holomorphic sectional curvatures constitute an integrable system as do Hamiltonian stationary Lagrangian surfaces in a 4-dimensional Hermitian symmetric space (this last being a result of Helein-Romon).

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