Killing Tensors on Tori
MFO Scientific ProgramResearch in Pairs 2016
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We show that Killing tensors on conformally at n-dimensional tori whose conformal factor only depends on one variable, are polynomials in the metric and in the Killing vector fields. In other words, every first integral of the geodesic flow polynomial in the momenta on the sphere bundle of such a torus is linear in the momenta.