Differential Geometry exam confusion!
Right, I need to show that a(t)=(cost,sint,0)is not a geodesic of the plane.
But I'm not sure what I'm supposed to actually do!
Right I've been thinking about the following
a regular curve on a surface is a geodesic of the surface is
So I need to get the unit tangent vector field to a(t)? which is
a'(t)=(-sint,cost,0) and ||a'(t)||=ROOT(sin^2(t)+cos^2(t))=1
n=(PHIu X PHIv)/||PHIu X PHIv||
I'm not sure where I'm going from here on in, I end up completely
confused with tons of definitions? Am I on the right track?
Any help much appreciated!