1. Mar 30, 2010 #1

   paweld

   

   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).

    

   paweld, Mar 30, 2010
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3. Mar 30, 2010 #2

   utesfan100

   

   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.

    

   utesfan100, Mar 30, 2010
4. Mar 30, 2010 #3

   hamster143

   

   Only if the metric tensor is nonsingular everywhere.

    

   hamster143, Mar 30, 2010

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