Killing tensors on tori
Differential Geometry
2017-12-21 v1
Abstract
We show that Killing tensors on conformally flat -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.
Keywords
Cite
@article{arxiv.1610.02009,
title = {Killing tensors on tori},
author = {Konstantin Heil and Andrei Moroianu and Uwe Semmelmann},
journal= {arXiv preprint arXiv:1610.02009},
year = {2017}
}
Comments
8 pages