Hamiltonian stationary Lagrangian tori contained in a hypersphere
Differential Geometry
2015-02-20 v8
Abstract
The Clifford torus is a torus in a three-dimensional sphere. Homogeneous tori are simple generalization of the Clifford torus which still in a three-dimensional sphere. There is a way to construct tori in a three-dimensional sphere using the Hopf fibration. In this paper, all Hamiltonian stationary Lagrangian tori which is contained in a hypersphere in the complex Euclidean plane are constructed explicitly. Then it is shown that they are homogeneous tori. For the construction, flat quaternionic connections of Hamiltonian stationary Lagrangian tori are considered and a spectral curve of an associated family of them is used.
Keywords
Cite
@article{arxiv.0710.4233,
title = {Hamiltonian stationary Lagrangian tori contained in a hypersphere},
author = {Katsuhiro Moriya},
journal= {arXiv preprint arXiv:0710.4233},
year = {2015}
}
Comments
This paper has been withdrawn by the author because the result is trivial