Special Lagrangian cones in C³ and primitive harmonic maps

الأصل · EN

In this article I show that every special Lagrangian cone in C³ determines, and is determined by, a primitive harmonic surface in the 6-symmetric space SU₃/SO₂. 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.