Special Lagrangians of cohomogeneity one in the resolved conifold

TL;DR

This paper classifies and describes specific special Lagrangian submanifolds with symmetry in the resolved conifold, revealing a foliation by T^2-invariant Lagrangians and families with SO(3) symmetry.

Contribution

It provides a detailed description of cohomogeneity one special Lagrangians in the resolved conifold, including a foliation by T^2-invariant Lagrangians and SO(3)-invariant families, extending previous work.

Findings

Foliation of the resolved conifold by T^2-invariant special Lagrangians

Existence of SO(3)-invariant special Lagrangian families

Asymptotic approach to the same Lagrangian cones in the conifold

Abstract

In this paper, which is a natural continuation of our previous paper math.DG/0504557, we describe some special Lagrangians of cohomogeneity one in the resolved conifold. Our main result gives a foliation of the resolved conifold by T^2-invariant special Lagrangians, where the generic leaf is topologically T^2 X R. We also obtain a family of SO(3)-invariant special Lagrangians. These special Lagrangian families in both the deformed and the resolved conifold approach asymptotically the same special Lagrangian cones in the conifold.