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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 -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