Hamiltonian stationary Lagrangian surfaces in Hermitian symmetric spaces

Details Hamiltonian stationary Lagrangian surfaces in Hermitian symmetric spaces Hamiltonian stationary Lagrangian surfaces in Hermitian symmetric spaces

2000-10-25

arxiv.org/abs/math/0010231v1

Mathematics

Differential Geometry

Scientific paper

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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