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 oneparameter 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 

Pages (fromto)  103111 
Journal  Journal of Geometry and Symmetry in Physics 
Volume  35 
Issue number  2014 
DOIs  
Publication status  Published  2014 
Bibliographical note
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Profiles

Robert Low
 School of Computing, Electronics and Maths  Reader in Mathematical Physics
Person: Teaching and Research