Toric Nearly K\"ahler manifolds

TL;DR

This paper characterizes 6-dimensional strict nearly Kähler manifolds with effective torus actions through a local description involving solutions to a Monge-Ampère type equation.

Contribution

It provides a local classification of such manifolds via a function satisfying a specific Monge-Ampère equation, linking geometric structure to PDE solutions.

Findings

Characterization of 6D strict nearly Kähler manifolds with T^3 symmetry

Local description via a Monge-Ampère type PDE

Complete local classification near each point

Abstract

We show that 6-dimensional strict nearly K\"ahler manifolds admitting effective $\mathbb{T}^3$ actions by automorphisms are completely characterized in the neigbourhood of each point by a function on $\mathbb{R}^3$ satisfying a certain Monge-Amp\`ere type equation.