Explicit expressions for the Iwasawa factors, the metric and the monodromy matrices for minimal Lagrangian surfaces in $\mathbb{C} P^2$

TL;DR

This paper derives explicit formulas for geometric quantities of minimal Lagrangian surfaces in complex projective space, focusing on equivariant cases and utilizing Weierstrass elliptic functions.

Contribution

It provides explicit expressions for Iwasawa factors, the metric, and monodromy matrices for minimal Lagrangian surfaces in  P^2, advancing the understanding of their geometric structure.

Findings

Explicit formulas for Iwasawa factors and monodromy matrices.

Characterization of rotationally and translationally equivariant minimal Lagrangian surfaces.

Use of Weierstrass elliptic functions in geometric descriptions.

Abstract

In this paper we continue our study of equivariant minimal Lagrangian surfaces in $\mathbb{C} P^2$, characterizing the rotationally equivariant cases and providing explicit formulae for relevant geometric quantities of translationally equivariant minimal Lagrangian surfaces in terms of Weierstrass elliptic functions.