regretfuljones
Oct28-04, 07:00 PM
Show that x1=asecx2 is a geodesic for the Euclidean metric in polar coordinates.
So I tried taking all the derivatives and plugging into polar geodesic equations. Obviously, bad idea.
Now I'm thinking I need to use Dgab/du=gab;cx'c and prove that the lengths of some vectors and their dot product are invariants under parallel transport, but I don't know how to go about doing that. Any advice on how to relate these concepts would be appreciated.
So I tried taking all the derivatives and plugging into polar geodesic equations. Obviously, bad idea.
Now I'm thinking I need to use Dgab/du=gab;cx'c and prove that the lengths of some vectors and their dot product are invariants under parallel transport, but I don't know how to go about doing that. Any advice on how to relate these concepts would be appreciated.