Christoffel Symbol on a Spherical Metric
Classical Mechanics
Level
3
\[ds^2 = r^2 \, d\theta^2 + \dfrac{1}{1+r^2} \sin^2 (\theta) \, d\phi^2\]
A strange metric on a sphere of radius \(r\) is given by the invariant interval described above.
Compute the Christoffel symbol \(\large \Gamma^{\phi}_{\phi \theta}\).
by
Matt DeCross