Let [tex]\gamma[/tex] be a stright line in a surface M. Prove [tex]\gamma[/tex] is a geodeisc
The Attempt at a Solution
In a plane we know a straight line is the shortest distance between two point. I am not sure if this applies to straight lines on a surface.
Further more, there is a theorem that says that if [tex]\gamma[/tex] is a unit speed curve and the shortest distance between two points P= [tex]\gamma (a)[/tex] and [tex]Q=\gamma (b)[/tex]then it is a geodesic.
But i do not know how to show some arbitrary straight line is unit speed or if this approach is even valid.
Any help appreciated.