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 …

Using a criterion of Johnson-Rees [9] we give a list of all four and six dimensional flat Kähler
manifolds. We calculate their R–cohomology, including the Hodge numbers. As a corollary …

Given a Hermitian line bundle L with a harmonic connection over a compact Riemann
surface (S, g) of constant curvature, we study the spectral geometry of the corresponding …

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Using a formula from Donnelly (Indiana Univ Math J 27 (6): 889–918, 1978), we prove that
for a family of seven dimensional flat manifolds with cyclic holonomy groups the η invariant …

We present a new description of the spectrum of the (spin-) Dirac operator D on lens spaces.
Viewing a spin lens space L as a locally symmetric space Γ \ Spin (2m)/Spin (2m-1) Γ\Spin …

In this paper we report on recent results by several authors, on the spectral theory of lens
spaces and orbifolds and similar locally symmetric spaces of rank one. Most of these results …

We obtain a simple formula for the multiplicity of eigenvalues of the Hodge-Laplace
operator, Δ f, acting on sections of the full exterior bundle Λ^*(TM)= p= 0^ n Λ^ p (TM) over …

An n-dimensional closed flat manifold is said to be of diagonal type if the standard
representation of its holonomy group G is diagonal. An n-dimensional Bieberbach group of …

We formulate a condition for the existence of a SpinC-structure on an oriented flat manifold
Mn with H2 (Mn, R)= 0. We prove that Mn has a SpinC-structure if and only if there exists a …