Families of strong KT structures in six dimensions

Abstract

This paper classifies Hermitian structures on 6-dimensional nilmanifolds $M=\Gamma \backslash G$ for which the fundamental 2-form is $\partial \bar{\partial }$-closed, a condition that is shown to depend only on the underlying complex structure $J$ of $M$. The space of such $J$ is described when $G$ is the complex Heisenberg group, and explicit solutions are obtained from a limaçon-shaped curve in the complex plane. Related theory is used to provide examples of various types of Ricci-flat structures.