In this paper, we describe the cohomogeneity one special Lagrangian 3-folds in both the deformed and the resolved conifolds. Our results give an explicit construction of the families of $SO(3)$ and $T^2$-invariant special Lagrangian submanifolds in these conifolds and describe their asymptotic behavior.
"Cohomogeneity one special Lagrangian 3-folds in the deformed and the resolved conifolds." Illinois J. Math. 52 (3) 839 - 865, Fall 2008. https://doi.org/10.1215/ijm/1254403718