Special Lagrangian cones in C^3 and primitive harmonic maps
Differential Geometry
2007-05-23 v2
Abstract
In this article I show that every special Lagrangian cone in C^3 determines, and is determined by, a primitive harmonic surface in the 6-symmetric space SU_3/SO_2. For cones over tori, this allows us to use the classification theory of harmonic tori to describe the construction of all the corresponding special Lagrangian cones. A parameter count is given for the space of these, and some examples found recently by Joyce are put into this context.
Cite
@article{arxiv.math/0201157,
title = {Special Lagrangian cones in C^3 and primitive harmonic maps},
author = {Ian McIntosh},
journal= {arXiv preprint arXiv:math/0201157},
year = {2007}
}
Comments
Version 2. LaTeX2e, 20 pages. Minor corrections and clarifications made. To appear in the Journal of the London Math Society