On Indefinite Special Lagrangian Submanifolds in Indefinite Complex Euclidean Spaces

TL;DR

This paper extends the concept of special Lagrangian submanifolds to indefinite complex Euclidean spaces, using calibrated geometry to identify minimal Lagrangian submanifolds in indefinite settings.

Contribution

It introduces indefinite special Lagrangian submanifolds in $C_k^m$ and generalizes Harvey-Lawson's work to the indefinite case.

Findings

Calibrated method detects indefinite minimal Lagrangian submanifolds.

Introduction of indefinite special Lagrangian submanifolds.

Generalization of Harvey-Lawson's work to indefinite spaces.

Abstract

In this paper, we show that the calibrated method can also be used to detect indefinite minimal Lagrangian submanifolds in $C_k^m$. We introduce the notion of indefinite special Lagrangian submanifolds in $C_k^m$ and generalize the well-known work of Harvey-Lawson to the indefinite case.