Periodic geodesics on compact riemannian manifolds

@article{Gromoll1969PeriodicGO,
  title={Periodic geodesics on compact riemannian manifolds},
  author={Detlef Gromoll and Wolfgang Meyer},
  journal={Journal of Differential Geometry},
  year={1969},
  volume={3},
  pages={493-510}
}
The interest in periodic geodesies arose at a very early stage of differential geometry, and has grown rapidly since then. It is a basic general problem to estimate the number of distinct periodic geodesies c: R —• Λί, c(t + 1) = c(t)9 on a complete riemannian manifold M in terms of topological invariants. Here periodic geodesies are always understood to be non-constant, and two such curves cl9 c2 will be said to be distinct if they are geometrically different, cx(R) Φ c£R). If M is non-compact… 
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