For two diierent integral forms K of the exceptional Jordan algebra we show that Aut K is generated by octave reeections. These providègeometric' examples of discrete reeection groups acting with nite covolume on the octave (or Cayley) hyperbolic plane O H 2 , the exceptional rank one symmetric space. (The isometry group of the plane is the exceptional Lie group F 4(?20) .) Our groups are deene...

We give a simplified proof of J. A. Wolf’s classification of finite groups that can act freely and isometrically on a round sphere of some dimension. We slightly improve the classification by removing some non-obvious redundancy. The groups are the same as the Frobenius complements of finite group theory. In chapters 4–7 of his famous Spaces of Constant Curvature [7], J. A. Wolf classified the ...

The structure of the general, inhomogeneous solution of (bosonic) Einstein-matter systems in the vicinity of a cosmological singularity is considered. We review the proof (based on ideas of BelinskiiKhalatnikov-Lifshitz and technically simplified by the use of the ArnowittDeser-Misner Hamiltonian formalism) that the asymptotic behaviour, as one approaches the singularity, of the general solutio...

Abstract. We present in this paper a C-metric on an open neighbourhood of the origin in R5. The metric is of Lorentzian signature (1, 4) and admits a solution to the twistor equation for spinors with a unique isolated zero at the origin. The metric is not conformally flat in any neighbourhood of the origin. The construction is based on the Eguchi-Hanson metric with parallel spinors on Riemannia...

In this article, we try to understand the mechanisms of the non properness of the action of the group of diffeomorphisms on the space of Lorentzian metrics of a compact manifold. We give a first result that describes the dynamical behavior of the sequences of diffeomorphisms involved which entails the existence of metrics that admit an isotropic geodesic foliation of codimension 1. On the 2-tor...

In this article, we try to understand the mechanisms of the non properness of the action of the group of diffeomorphisms on the space of Lorentzian metrics of a compact manifold. We give a first result that describes the dynamical behavior of the sequences of diffeomorphisms involved which entails the existence of metrics that admit an isotropic geodesic foliation of codimension 1. On the 2-tor...

We consider a simplicial minisuperspace modelling wormhole configurations. Such configurations result from a cut and paste procedure on two identical copies of the most relevant triangulation of our universe, namely the cone over α4, which is the simplest triangulation of S. The connecting space where the two copies are glued, acts as the throat of a wormhole connecting two distinct universes. ...