In this paper we determine and classify all compact Riemannian flat manifolds with holonomy group isomorphic to Z2 ⊕ Z2 and first Betti number zero. Also we give explicit realizations of all of them.

Let Γ1 and Γ2 be Bieberbach groups contained in the full isometry group G of Rn. We provethat if the compact flat manifolds Γ1\Rn and Γ2\Rn are strongly isospectral, then the Bieberbachgroups Γ1 and Γ2 are representation ...

It is the main purpose of this lecture to indicate a rather general method to construct quaternion-Kahler compact flat manifolds. This construction will give many families of quaternion Kahler manifolds of dimensions 8 or ...

We compute the eta function #x03B7;(s) and its corresponding η-invariant for the Atiyah–Patodi–Singer operator D acting on an orientable compact flat manifold of dimension =4h−1, ≥1, and holonomy group F≃Z2r , r∈N. We show ...

For any n≥7n≥7, k≥3k≥3, we give pairs of compact flat nn-manifolds MM, M′M′ with holonomy groups Zk2Z2k, that are strongly isospectral, hence isospectral on pp-forms for all values of pp, having nonisomorphic cohomology ...