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...
Prove that if tauijkl is a tensor such that, in the {xi}-system, tauijkl=3tauiljk , then tauijkl=3 tauiljkin all coordinate systems.
How would one go about proving this for all coordinate systems?