Crystallographic groups are groups which act in a nice way and via isometries on some n-
dimensional Euclidean space. They got their name, because in three dimensions they occur …

It is known that to any Riemannian manifold (M, g), with or without boundary, one can
associate certain fundamental objects. Among them are the Laplace-Beltrami opera tor and …

We study the family of closed Riemannian n-manifolds with holonomy group isomorphic to Z
n− 1 2, which we call generalized Hantzsche-Wendt manifolds. We prove results on their …

We study isospectrality on p-forms of compact flat manifolds by using the equivariant
spectrum of the Hodge-Laplacian on the torus. We give an explicit formula for the multiplicity …

Let $ M $ be an orientable compact flat Riemannian manifold endowed with a spin structure.
In this paper we determine the spectrum of Dirac operators acting on smooth sections of …

We compare and contrast various length vs Laplace spectra of compact flat Riemannian
manifolds. As a major consequence we produce the first examples of pairs of closed …

We give an explicit formula for the multiplicities of the eigenvalues ofthe Laplacian acting on
sections of natural vector bundles over acompact flat Riemannian manifold M Γ= Γ\ℝ n, Γ a …

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The aim of this text is to provide a clear description of the theory of Infra-nilmanifolds and
their fundamental groups, the almost-Bieberbach groups. For most of the proofs of the …

An n-dimensional Hantzsche-Wendt group is an n-dimensional orientable Bieberbach group
with holonomy group Zn− 12. We develop an algorithm that computes the homology of any …