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Andrei Moroianu: Lectures

September 10, 2019
TITLE: Toric nearly Kähler 6-manifolds

ABSTRACT: Nearly Kähler manifolds are a particular class of almost Hermitian manifolds in the Gray-Hervella classification, but for several reasons they are mostly relevant in dimension 6, where (normalized, strict) nearly Kähler 6-manifolds can be characterized by the fact that their metric cone has holonomy contained in \mathrm{G}_2. In this talk, based on a joint work with P.-A. Nagy, I will show that strict nearly Kähler 6-manifolds admitting effective \mathbb{T}^3 actions by automorphisms are characterized in the neigbourhood of each point by a function on \mathbb{R}^3 satisfying a certain Monge–Ampère-type equation.