Families of strong KT structures in six dimensions

Abstract

This paper classifies Hermitian structures on 6-dimensional nilmanifolds $M=\Ga\bs G$ for which the fundamental 2-form is $\pd\opd$-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.