In order to characterize the systems of second-order ODEs which admit a regular Lagrangian function, Noether symmetries for the geodesic equations of the canonical linear connection on Lie groups of dimension three or less are obtained, so the characterization of these geodesic equations through their Noethers symmetries Lie Algebras is investigated. The corresponding conservation laws and the first integral for each geodesics are constructed.
A. Ghanam, Ryad and Y. Al-Dweik, Ahmad
"Conservation laws for the geodesic equations of the canonical connection on Lie groups in dimensions two and three,"
Applied Mathematics & Information Sciences: Vol. 07:
1, Article 39.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss1/39