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Lie symmetries of geodesic equations and projective collineations

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Abstract

We prove a theorem which relates the Lie symmetries of the geodesic equations in a Riemannian space with the collineations of the metric. We apply the results to Einstein spaces and spaces of constant curvature. Finally with examples we show the use of the results.

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Authors and Affiliations

  1. Department of Physics, Section of Astronomy-Astrophysics-Mechanics, University of Athens, Panepistemiopolis, Athens, 157 83, Greece

    Michael Tsamparlis & Andronikos Paliathanasis

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  1. Michael Tsamparlis
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  2. Andronikos Paliathanasis
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Correspondence to Michael Tsamparlis.

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Tsamparlis, M., Paliathanasis, A. Lie symmetries of geodesic equations and projective collineations. Nonlinear Dyn 62, 203–214 (2010). https://doi.org/10.1007/s11071-010-9710-x

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  • DOI: https://doi.org/10.1007/s11071-010-9710-x

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