Hamiltonian stationary Lagrangian surfaces in Hermitian symmetric spaces

Abstract : This paper is the third of a series on Hamiltonian stationary Lagrangian surfaces. We present here the most general theory, valid for any Hermitian symmetric target space. Using well-chosen moving frame formalism, we show that the equations are equivalent to an integrable system, generalizing the C^2 subcase analyzed in the first article (arXiv:math.DG/0009202). This system shares many features with the harmonic map equation of surfaces into symmetric spaces, allowing us to develop a theory close to Dorfmeister, Pedit and Wu's, including for instance a Weierstrass-type representation. Notice that this article encompasses the article mentioned above, although much fewer details will be given on that particular flat case.
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https://hal.archives-ouvertes.fr/hal-00739688
Contributor : Pascal Romon <>
Submitted on : Monday, October 8, 2012 - 4:21:49 PM
Last modification on : Wednesday, September 4, 2019 - 1:52:03 PM

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Frédéric Hélein, Pascal Romon. Hamiltonian stationary Lagrangian surfaces in Hermitian symmetric spaces. Mathematical Society of Japan 9thInternational Research Institute on Integrable Systems in Differential Geometry, 2000, Tokyo, Japan. pp.161-178. ⟨hal-00739688⟩

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