Spectral data for Hamiltonian-minimal Lagrangian tori in $CP^2$

TL;DR

This paper develops a spectral data framework using theta functions to identify Hamiltonian-minimal Lagrangian tori in complex projective space, advancing the understanding of their geometric structure.

Contribution

It introduces a novel spectral data approach for constructing Hamiltonian-minimal Lagrangian tori in $CP^2$ using spectral curves and theta functions.

Findings

Spectral data characterized for Hamiltonian-minimal Lagrangian tori

Explicit theta function representations derived

Enhanced methods for studying Lagrangian submanifolds in complex projective spaces

Abstract

In this work, we find spectral data that allow to find Hamiltonian-minimal Lagrangian tori in $CP^2$ in terms of theta functions of spectral curves.