# 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}
}```
• Published 1969
• Mathematics
• Journal of Differential Geometry
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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