Session S23 - Group actions in Differential Geometry

Friday, July 16, 17:20 ~ 17:50 UTC-3

The geodesic flow on Lie groups

Gabriela Paola Ovando

Universidad Nacional de Rosario and CONICET, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The goal is the study of the integrability of the geodesic flow on Lie groups, when equipped with a left-invariant metric. We study Liouville integrability, specially on nilpotent Lie groups of steps two and three. It is shown that complete families of first integrals can be constructed with Killing vector fields and symmetric Killing 2-tensor fields. This holds for several families in dimensions up to six. Several algebraic relations on the Lie algebra of first integrals can be explicitly written. Also invariant first integrals are analyzed and several involution conditions are shown. With time, we shall see some kind of generalizations.

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