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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 10: Classical and quantum gravity

MP 10.3: Vortrag

Donnerstag, 24. März 2022, 16:55–17:15, MP-H5

Local normal forms for Riemannian metrics with infinitesimal symmetries of their pre-geodesics. — •Andreas Vollmer — Corso Duca degli Abruzzi, 24, 10129 Torino TO Italy

Projective vector fields are infinitesimal symmetries that preserve pre-geodesics, i.e. geodesics up to reparametrisation. A classical problem formulated by Sophus Lie is to describe the local metrics that admit such symmetries.

The list of local normal forms in dimension two has only recently been established, by Aminova (1990, 2003), Bryant-Manno-Matveev (2009), Matveev (2012) and Manno-V (2020). In joint work with G. Manno, we have recently derived such a list for dimension three, too (arXiv:2110.06785). The talk will provide an overview of the normal forms and their projective symmetry algebras, and will explain the techniques used to obtain them.