Special Lagrangian m-folds in C^m with symmetries

Journal article

This is the first in a series of papers on special Lagrangian submanifolds in C^m. We study special Lagrangian submanifolds in C^m with large symmetry groups, and give a number of explicit constructions. Our main results concern special Lagrangian cones in C^m invariant under a subgroup G in SU(m) isomorphic to U(1)^{m-2}. By writing the special Lagrangian equation as an o.d.e. in G-orbits and solving the o.d.e., we find a large family of distinct, G-invariant special Lagrangian cones on T^{m-1} in C^m. These examples are interesting as local models for singularities of special Lagrangian submanifolds of Calabi-Yau manifolds. Such models will be needed to understand Mirror Symmetry and the SYZ conjecture.

Authors: Joyce, D

• Publication status: Published
• Journal: Duke Mathematical Journal 115 (2002), 1-51.
• Volume: 115
• Issue: 1
• Pages: 1-51
• Publication date: 2000-08-02
• DOI: 10.1215/S0012-7094-02-11511-7
• ISSN: 0012-7094
• Keywords: math.DG