# A construction of special Lagrangian submanifolds by generalized perpendicular symmetries

## TL;DR

This paper introduces a novel method for constructing special Lagrangian submanifolds in Calabi-Yau manifolds using generalized perpendicular symmetries and moment maps, enabling the creation of new non-trivial examples in non-flat settings.

## Contribution

It presents a new construction technique leveraging Lie group actions and moment maps, expanding the class of known special Lagrangian submanifolds in Calabi-Yau manifolds.

## Key findings

- Constructed non-trivial special Lagrangian submanifolds in cotangent bundles of spheres.
- Demonstrated the use of non-abelian Lie group actions in the construction process.
- Provided explicit examples in non-flat Calabi-Yau manifolds with Stenzel metrics.

## Abstract

We show a method to construct a special Lagrangian submanifold L' from a given special Lagrangian submanifold L in a Calabi-Yau manifold with the use of generalized perpendicular symmetries. We use moment maps of the actions of Lie groups, which are not necessarily abelian. By our method, we construct some non-trivial examples in the cotangent bundles of the spheres which are non-flat Calabi-Yau manifolds equipped with the Stenzel metrics.