Curved manifolds with conserved Runge-Lenz vectors
arXiv:0908.1204 · doi:10.1063/1.3266874
Abstract
van Holten's algorithm is used to construct Runge-Lenz-type conserved quantities, induced by Killing tensors, on curved manifolds. For the generalized Taub-NUT metric, the most general external potential such that the combined system admits a conserved Runge-Lenz-type vector is found. In the multi-center case, the subclass of two-center metric exhibits a conserved Runge-Lenz-type scalar.
20 pages
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