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Lines on manifolds

  1. Jun 19, 2013 #1
    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.
  2. jcsd
  3. Jun 19, 2013 #2
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