Abstract
Stationary geodesics of left-invariant Riemannian metrics on Lie groups were introduced by Arnold as those geodesics which are also orbits of one-parameter groups of left-translations. The existence of infinitely many stationary geodesics in the case of compact semi-simple Lie groups has recently been established by Szenthe J. Stationary geodesics of left-invariant Lagrangians on Lie groups are studied and the existence of infinitely many such geodesics on compact semi-simple Lie groups is established below.
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