English

Killing tensors on tori

Differential Geometry 2017-12-21 v1

Abstract

We show that Killing tensors on conformally flat nn-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

R2 v1 2026-06-22T16:13:31.484Z