Mathematics – Differential Geometry
Scientific paper
2000-08-02
Duke Mathematical Journal 115 (2002), 1-51.
Mathematics
Differential Geometry
44 pages, LaTeX; (v4) minor corrections and improvements
Scientific paper
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.
No associations
LandOfFree
Special Lagrangian m-folds in C^m with symmetries does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Special Lagrangian m-folds in C^m with symmetries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Special Lagrangian m-folds in C^m with symmetries will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-403170