Isospectrality of Flat Lorentz 3-Manifolds

Flat Lorentz 3 - manifolds and cocompact

Flat Lorentz 3-manifolds and cocompact Fuchsian groups

Mess deduces this result as part of a general theory of domains of dependence in constant curvature Lorentzian 3-manifolds. We give an alternate proof, using an invariant introduced by Margulis [18, 19] and Teichmüller theory. We thank Scott Wolpert for helpful conversations concerning Teichmüller theory. We also wish to thank Paul Igodt and the Algebra Research Group at the Katholieke Universi...

Low dimensional flat manifolds with some classes of Finsler metric

Flat Riemannian manifolds are (up to isometry) quotient spaces of the Euclidean space R^n over a Bieberbach group and there are an exact classification of of them in 2 and 3 dimensions. In this paper, two classes of flat Finslerian manifolds are stuided and classified in dimensions 2 and 3.

Isospectrality and 3-manifold Groups

In this note, we explain how a well-known construction of isospectral manifolds leads to an obstruction to a group being the fundamental group of a closed 3-dimensional manifold. The problem of determining, for a given group G, whether there is a closed 3-manifold M with π1(M) ∼= G is readily seen to be undecidable; let us write G ∈ G 3 if there is such a 3-manifold. A standard conjecture (rela...

3-manifolds Which Are Spacelike Slices of Flat Spacetimes

We continue work initiated in a 1990 preprint of Mess giving a geometric parameterization of the moduli space of classical solutions to Einstein’s equations in (2 + 1) dimensions with cosmological constant Λ = 0 or −1 (the case Λ = +1 has been worked out in the interim by the present author). In this paper we make a first step toward the (3 + 1)-dimensional case by determining exactly which clo...