Generalized Hantzsche-Wendt flat manifolds

Abstract

We study the family of closed Riemannian $n$-manifolds with holonomy group isomorphic to ${\mathbb{Z}}_2^{n-1}$, which we call generalized Hantzsche-Wendt manifolds. We prove results on their structure, compute some invariants, and find relations between them, illustrated in a graph connecting the family.