This talk is about homogeneous manifolds M equipped with a pseudo-Riemannian (i.e. indefinite) metric tensor, such that M = G/H for a Lie group G which acts transitively and isometrically on M, where H is a cocompact subgroup of G. We will see how density properties of H restrict the structure of G and the metric on M. A first special case are those M with solvable group G. Here, it turns out that H is a lattice in G and M is a locally symmetric space. This leads to the case groups G of arbitrary types, which is complicated by the existence of compact semisimple factors. I will also briefly address the existence of Einstein metrics in this class of manifolds. This talk is based on joint works with Oliver Baues, Yuri Nikolayevsky and Abdelghani Zeghib.
The University of Adelaide
Tue, 16/08/2016 - 12:00pm to 1:00pm
RC-4082, The Red Centre, UNSW