We construct examples of cohomogeneity one special Lagrangian submanifolds in the cotangent bundle over the complex projective space, whose Calabi-Yau structure was given by Stenzel. For each example, we describe the condition of special Lagrangian as an ordinary differential equation. Our method is based on a moment map technique and the classification of cohomogeneity one actions on the complex projective space classified by Takagi.
"Special Lagrangian Submanifolds and Cohomogeneity One Actions on the Complex Projective Space." Tokyo J. Math. 42 (1) 255 - 284, June 2019. https://doi.org/10.3836/tjm/1502179289