Open Access
2014 A Generalized Clairaut's Theorem in Minkowski Space
Ansi Saad, Robert J. Low
J. Geom. Symmetry Phys. 35: 103-111 (2014). DOI: 10.7546/jgsp-35-2014-103-111


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.


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Ansi Saad. Robert J. Low. "A Generalized Clairaut's Theorem in Minkowski Space." J. Geom. Symmetry Phys. 35 103 - 111, 2014.


Published: 2014
First available in Project Euclid: 27 May 2017

zbMATH: 1328.53013
MathSciNet: MR3380902
Digital Object Identifier: 10.7546/jgsp-35-2014-103-111

Rights: Copyright © 2014 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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