Riemannian Manifolds: Extending Geodesics Indefinitely

Dragonfall · Jun 19, 2013

Given a closed Riemannian manifold, a point P on it and a nonzero vector V in its tangent space, can you extend a geodesic in that direction of V indefinitely? I count looping back onto itself as "indefinitely".

The theorem I have in my book only guarantees that this is possible locally near P.

micromass · Jun 19, 2013

https://www.physicsforums.com/showthread.php?t=696582

Riemannian Manifolds: Extending Geodesics Indefinitely

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Riemannian Manifolds: Extending Geodesics Indefinitely

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