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Special Lagrangian cones in C^3 and primitive harmonic maps

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Publication details

JournalJournal of the london mathematical society-Second series
DatePublished - 27 Jun 2002
Issue number3
Number of pages21
Pages (from-to)769-789
Original languageEnglish


It is shown that every special Lagrangian cone in C-3 determines, and is determined by, a primitive harmonic surface in the 6-symmetric space SU3/SO2. For cones over tori, this allows the classification theory of harmonic tori to be used to describe the construction of all the corresponding special Lagrangian cones. A parameter count is given for the space of these, and some of the examples found recently by Joyce are put into this context.

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