Q: Geodesic equation and radial metric Assume that $g(z)=f(|z|)$ is a radial metric on the unit disk in complex plane, where $f$ is a smooth real function. Is there any simple equation of geodesic lines w.r.t. metric $g$, e.g. $g(t)=1/\sqrt{1-|t|^2}$. I am interested on the metric $$d_g(z,w)=\inf_{z,w\in\gamma}\int_\gamma\frac{1}{\sqrt{1-|t|^2}}dt$$
