Hamiltonian stationary Lagrangian surfaces in Hermitian symmetric spaces
Differential Geometry
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0010231,
title = {Hamiltonian stationary Lagrangian surfaces in Hermitian symmetric spaces},
author = {Frederic Helein and Pascal Romon},
journal= {arXiv preprint arXiv:math/0010231},
year = {2007}
}