### Abstract

In Euclidean space, the geodesics on a surface of revolution can be characterized
by means of Clairaut’s theorem, which essentially says that the geodesics
are curves of fixed angular momentum. A similar result is known for three dimensional
Minkowski space for timelike geodesics on surfaces of revolution about the
time axis. Here, we extend this result to consider generalizations of surfaces of revolution
to those surfaces generated by any one-parameter subgroup of the Lorentz
group. We also observe that the geodesic flow in this case is easily seen to be a completely
integrable system, and give the explicit formulae for the timelike geodesics.

Original language | English |
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Pages (from-to) | 103-111 |

Journal | Journal of Geometry and Symmetry in Physics |

Volume | 35 |

Issue number | 2014 |

DOIs | |

Publication status | Published - 2014 |

### Bibliographical note

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## Cite this

Saad, A., & Low, R. (2014). A generalized Clairaut's theorem in Minkowski space.

*Journal of Geometry and Symmetry in Physics*,*35*(2014), 103-111. https://doi.org/10.7546/jgsp-35-2014-103-111