On product minimal Lagrangian submanifolds in complex space forms

TL;DR

This paper classifies minimal Lagrangian submanifolds in complex space forms that are Riemannian products of two manifolds with constant sectional curvature, providing a comprehensive understanding of their structure.

Contribution

It offers a complete classification of product minimal Lagrangian submanifolds in complex space forms, a previously unresolved problem.

Findings

Classification of such submanifolds is achieved.

Characterization of the geometric structure of these submanifolds.

Insights into the curvature properties of the components.

Abstract

In this paper we consider minimal Lagrangian submanifolds in $n$-dimensional complex space forms. More precisely, we study such submanifolds which, endowed with the induced metrics, write as a Riemannian product of two Riemannian manifolds, each having constant sectional curvature. As the main result, we give a complete classification of these submanifolds.