(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let [tex]\gamma[/tex] be a stright line in a surface M. Prove [tex]\gamma[/tex] is a geodeisc

3. 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.

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# Homework Help: Geodesics and straight lines on a surface

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