Special Lagrangian cones in C^3 and primitive harmonic maps

I McIntosh

doi:10.1112/S0024610703004204

Special Lagrangian cones in C^3 and primitive harmonic maps

I McIntosh

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	769-789
Number of pages	21
Journal	Journal of the london mathematical society-Second series
Volume	67
Issue number	3
DOIs	https://doi.org/10.1112/S0024610703004204
Publication status	Published - 27 Jun 2002

Keywords

MINIMAL TORI

Access to Document

10.1112/S0024610703004204

http://dx.doi.org/10.1112/S0024610703004204

Cite this

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title = "Special Lagrangian cones in C^3 and primitive harmonic maps",

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AB - 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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DO - 10.1112/S0024610703004204

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