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MINIMAL LAGRANGIAN 2-TORI IN $\mathbb{CP}^2$ COME IN REAL FAMILIES OF EVERY DIMENSION

Published online by Cambridge University Press:  29 March 2004

EMMA CARBERRY  and
IAN MCINTOSH
EMMA CARBERRY
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USAcarberry@math.mit.edu
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 for every non-negative integer $n$, there is a real $n$-dimensional family of minimal Lagrangian tori in $\mathbb{CP}^2$, and hence of special Lagrangian cones in $\mathbb{C}^3$ whose link is a torus. The proof utilises the fact that such tori arise from integrable systems, and can be described using algebro-geometric (spectral curve) data.

Keywords

53C4358E20
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 531 - 544
Copyright
The London Mathematical Society 2004

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