Can an incomplete geodesic intersect a point infinitely many times?

differential-geometry general-relativity geodesic semi-riemannian-geometry

Solution 1:

The Clifton-Pohl torus is an example of a compact Lorentzian manifold which is not geodesically complete: more than that, there exists a closed geodesic which is not complete!

(Community wiki as it is a link only answer)

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