# 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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