A semi-Riemannian manifold is a manifold whose tangent bundle carries a non-degenerate quadratic form. Such a quadratic form induces a geodesic flow, but unlike in Riemannian geometry, on a compact manifold, this flow may not be complete. However, it is conjectured that this flow is complete when the metric is locally symetric. Here we address this conjecture for compact manifolds modelled on a rank 1 Lie group with its Killing metric. In this geometry, compact complete manifolds have been described by works of Guéritaud, Guichard, Kassel and Wienhard. We will prove that those complete manifolds cannot be continuously deformed into non complete ones. For this, we will adopt Thurston formalism of the notion of (G,X)-structure.
Dienstag, den 22. Oktober 2013 um 13.30 Uhr, in INF 288, HS 5 Dienstag, den 22. Oktober 2013 at 13.30, in INF 288, HS 5
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Anna Wienhard