6 May 2011; IMS (UiTø), room U1=A228. Friday 12:15-14:00.

Aleksandra Fedorova (Friedrich-Schiller-Universität Jena, Germany)

“Geodesic mobility of Lorentzian metrics”

Two pseudo-Riemannian metrics are called geodesically equivalent if their geodesics coincide as unparametrized curves. The dimension of the space of metrics geodesically equivalent to the metric g is called the degree of geodesic mobility of g.

The theory of geodesically equivalent metrics is rather old. The first description of the pair of geodesically equivalent metrics has been given by Levi-Civita, but the PDE he obtained is essentially nonlinear and has a complicated structure. Recent results obtained by Shandra (2000), Matveev and Kiosak (2009-2010) show that the degree of geodesic mobility is strongly related to the number of covariantly constant tensors on the so-called cone manifold. Thus one can calculate degree of geodesic mobility with the help of linear algebraic methods.

In our work we generalize the result of Shandra, who calculated all possible values of degree of geodesic mobility of Riemannian metric, to the Lorentzian case.