Homogeneous Lagrangian submanifolds of positive Euler characteristic

TL;DR

This paper classifies all homogeneous Lagrangian submanifolds with positive Euler characteristic in complex Grassmannians, providing a complete understanding of their structure and symmetry.

Contribution

It offers the first complete classification of homogeneous Lagrangian submanifolds with positive Euler characteristic in complex Grassmannians.

Findings

Identified all such submanifolds as group orbits.

Established their geometric and topological properties.

Provided explicit descriptions of these submanifolds.

Abstract

We fully classify all Lagrangian submanifolds of a complex Grassmannian which are an orbit of a compact group of isometries and have positive Euler characteristic.