A family of conformally flat Hamiltonian-minimal Lagrangian tori in $\mathbb{CP}^3$

TL;DR

This paper constructs a family of conformally flat Hamiltonian-minimal Lagrangian tori in complex projective 3-space using a reduction method involving the Hopf map and a specific map from three-dimensional space.

Contribution

It introduces a novel construction of Hamiltonian-minimal Lagrangian tori in b^3 via a reduction approach involving the Hopf map and conformal flatness.

Findings

Explicit family of tori constructed

Uses reduction via Hopf map and b^3 mapping

Contributes to understanding of Lagrangian submanifolds in b^3

Abstract

In this paper by reduction we construct a family of conformally flat Hamiltonian-minimal Lagrangian tori in $\mathbb{CP}^3$ as the image of the composition of the Hopf map $\mathcal{H}: \mathbb{S}^7\to \mathbb{CP}^3$ and a map $\psi:\mathbb{R}^3 \to \mathbb{S}^7$ with certain conditions.