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Null geodesic in 2 dimensional manifold

  1. Mar 30, 2010 #1
    I have a question. Is it true that any curve in 2-dimensional manifold which tangent vector is null at each point is null geodesic? (In 2-dimensional manifold there are only 2 null direcitions at each point).
  2. jcsd
  3. Mar 30, 2010 #2
    For a perfect donut sitting flat on a table, the circle of contact is a curve on the torus. I may be wrong, but isn't that such a curve without being a null geodesic?

    I will now eat the perfect donut.
  4. Mar 30, 2010 #3
    Only if the metric tensor is nonsingular everywhere.
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