Special Lagrangian cones in C^3 and primitive harmonic maps
arXiv:math/0201157
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.
Version 2. LaTeX2e, 20 pages. Minor corrections and clarifications made. To appear in the Journal of the London Math Society