Nonlinear Dynamics

, Volume 62, Issue 1–2, pp 203–214 | Cite as

Lie symmetries of geodesic equations and projective collineations

  • Michael Tsamparlis
  • Andronikos Paliathanasis
Original Paper


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.


Geodesics General relativity theory Classical mechanics Collineations Riemannian space Autoparallels Lie symmetries Projective collineations 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Physics, Section of Astronomy-Astrophysics-MechanicsUniversity of AthensAthensGreece

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