# Special Lagrangian submanifolds and cohomogeneity one actions on the complex projective space

## TL;DR

This paper constructs specific cohomogeneity one special Lagrangian submanifolds in the cotangent bundle of complex projective space using moment map techniques and classifies their conditions via differential equations.

## Contribution

It introduces new examples of special Lagrangian submanifolds in a Calabi-Yau setting and provides a method to analyze their properties through differential equations.

## Key findings

- Explicit examples of cohomogeneity one special Lagrangian submanifolds.
- Differential equations characterizing the special Lagrangian condition.
- Application of moment map techniques in the classification process.

## Abstract

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.