Special Lagrangian cones in C^3 and primitive harmonic maps

Details Special Lagrangian cones in C^3 and primitive harmonic maps Special Lagrangian cones in C^3 and primitive harmonic maps

2002-01-17

arxiv.org/abs/math/0201157v2

J. London Math. Soc (3) 67 (2003) 769-789

Mathematics

Differential Geometry

Version 2. LaTeX2e, 20 pages. Minor corrections and clarifications made. To appear in the Journal of the London Math Society

Scientific paper

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.

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