Let gamma be a straight line in a surface M. How can we prove that gamma is a geodesic?
ALl I note is that a geodesic on a surface M is a unit speed curve on M with geodesic curvature = 0 everywhere.
Update: To making it not look like the question is a tautology, check out this:
http://www.physicsforums.com/showthread.php?t=407105
I'm trying to fill in the gaps and understand the argument for proving this theorem. Thanks