A Construction of Special Lagrangian Submanifolds by Generalized Perpendicular Symmetries

Abstract

We show a method to construct a special Lagrangian submanifold $L^\prime$ 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 non-flat Calabi-Yau manifolds $\mathrm{T}^\ast S^n$ which equipped with the Stenzel metrics.