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Special Lagrangian cones in C3 and primitive harmonic maps

2002/01/31 by Ian McIntosh
Mathematics · #math.DG #msc:58E20 #msc:53C43

paper · pdf

published as J. London Math. Soc (3) 67 (2003) 769-789 · Version 2. LaTeX2e, 20 pages. Minor corrections and clarifications made. To appear in the Journal of the London Math Society

arxiv created 2002/07/02 · arxiv updated 2009/11/30

Abstract

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.

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