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Minimal Lagrangian 2‐Tori in CP 2 Come in Real Families of Every Dimension
Author(s) -
Carberry Emma,
Mcintosh Ian
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703005039
Subject(s) - torus , lagrangian , dimension (graph theory) , mathematics , integer (computer science) , integrable system , pure mathematics , combinatorics , mathematical analysis , geometry , computer science , programming language
It is shown that for every non‐negative integer n , there is a real n ‐dimensional family of minimal Lagrangian tori in CP 2 , and hence of special Lagrangian cones in 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.