Tight Lagrangian surfaces in $S^2 \times S^2$

TL;DR

This paper classifies all tight Lagrangian surfaces in the product of two 2-spheres, showing that the only globally tight examples are the real forms, thus providing a complete characterization.

Contribution

It provides a complete classification of tight Lagrangian surfaces in $S^2 imes S^2$, identifying real forms as the only globally tight examples.

Findings

All tight Lagrangian surfaces in $S^2 imes S^2$ are classified.

Globally tight Lagrangian surfaces are exactly the real forms.

The classification completes the understanding of tight Lagrangian surfaces in this setting.

Abstract

We determine all tight Lagrangian surfaces in $S^2 \times S^2$. In particular, globally tight Lagrangian surfaces in $S^2 \times S^2$ are nothing but real forms.