Special Lagrangian submanifolds in C^n with flat and Fubini-Study metrics

TL;DR

This paper establishes conditions under which special Lagrangian submanifolds in complex Euclidean space also remain special Lagrangian when considered with the Fubini-Study metric, linking two geometric structures.

Contribution

It provides a necessary and sufficient criterion for a Lawlor-constructed special Lagrangian submanifold to be also special Lagrangian under the Fubini-Study metric.

Findings

Derived a precise condition for the dual special Lagrangian property

Connected the geometry of Lawlor submanifolds with Fubini-Study metrics

Enhanced understanding of Lagrangian submanifolds in different metric contexts

Abstract

We give a necessary and sufficient condition for a special Lagrangian submanifold in C^n constructed by Lawlor being also special Lagrangian in C^n with the Fubini-Study form.