Hello, I was wondering the following.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose you start with a Riemannian manifold M. Say you knowonegeodesic.

Pushing this geodesic forward through an isometry M -> M gives again a geodesic.

Can this procedure give youallgeodesics?

Thinking of the plane or the sphere it seems obviously true.

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# Are any two geodesics the same after applying an isometry?

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