**SMS scnews item created by Stephan Tillmann at Tue 15 Sep 2015 0857**

Type: Seminar

Distribution: World

Expiry: 15 Dec 2015

**Calendar1: 16 Sep 2015 1100-1200**

**CalLoc1: Carslaw 535A**

Auth: tillmann@p710.pc (assumed)

### Geometry & Topology

# Geodesic completeness of compact Lorentzian manifolds

### Thomas Leistner (Adelaide)

Wednesday 16 September 2015 from 11:00–12:00 in Carslaw 535A

Please join us for lunch after the talk!

**Abstract:**
A semi-Riemannian manifold is geodesically complete (or for short, complete)
if its maximal geodesics are defined for all times. For Riemannian metrics
the compactness of the manifold implies completeness. In contrast, there are
very simple compact Lorentzian manifolds that are not complete.
Nevertheless, completeness plays an important role for fundamental geometric
questions in Lorentzian geometry such as the classification of compact
Lorentzian manifolds of constant curvature and in particular for a
Lorentzian version of Bieberbach's theorem.
We will study the completeness for compact manifolds that arise from the
classification of Lorentzian holonomy groups, which we will briefly review
in the talk. These manifolds carry a parallel null vector field that can be
used to study their completeness. They include the co-called plane fronted
waves for which we determine the universal covering and show that they are
complete. In the talk we will explain this result and further work in
progress, both being joint work with A. Schliebner (Humboldt-Un