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 $\large \Gamma^{\phi}_{\phi \theta}$ .