On indefinite special Lagrangian submanifolds in indefinite complex Euclidean spaces

Abstract

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