Null geodesic in 2 dimensional manifold

  • Thread starter paweld
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  • #1
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Main Question or Discussion Point

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).
 

Answers and Replies

  • #2
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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.
 
  • #3
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Only if the metric tensor is nonsingular everywhere.
 

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