Veranstaltung

Vortrag
How to Reconstruct a Metric by its Unparameterized Geodesics
Vladimir Matveev
9.1.2012, 16:30 Uhr – 17:30 Uhr

We discuss whether it is possible to reconstruct a metric by its unparameterized geodesics, and how to do it effectively. We explain why this problem is interesting for general relativity. We show how to understand whether all curves from a sufficiently big family are unparameterized geodesics of a certain affine connection, and how to reconstruct algorithmically a generic 4-dimensional metric by its unparameterized geodesics. The algorithm works most effectively if the metric is Ricci-flat. We also prove that almost every metric does not allow nontrivial geodesic equivalence, and construct all pairs of 4-dimensional geodesically equivalent metrics of Lorenz signature. If the time allows, I will also explain how this theory helped to solve two problems explicitly formulated by Sophus Lie in 1882, and the semi- Riemannian two-dimensional version of the projective Lichnerowicz-Obata conjecture.
The new results of the talk are based on the papers
arXiv:1010.4699, arXiv:1002.3934, arXiv:0806.3169, arXiv:0802.2344, arXiv:0705.3592 joint with Bryant, Bolsinov, Kiosak, Manno, Pucacco.

Verknüpft mit:

• Vladimir Matveev