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SPECIAL LAGRANGIAN CONES IN $\C^3$ AND PRIMITIVE HARMONIC MAPS

Published online by Cambridge University Press:  20 May 2003

IAN McINTOSH
IAN McINTOSH
Affiliation:
Department of Mathematics, University of York, Heslington, York YO10 5DD im7@york.ac.uk
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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 ${\rm SU}_3/{\rm SO}_2$. 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.

Keywords

53C4358E20
Type
Research Article
Information
Journal of the London Mathematical Society , Volume 67 , Issue 3 , June 2003 , pp. 769 - 789
Copyright
The London Mathematical Society 2003

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