Let \((M,g)\) be a Riemannian manifold and \(\gamma:(a,b)\to M\) a geodesic. Then \(\gamma\) is parameterized by constant speed.
We have
\begin{equation} \frac{d}{dt}|\gamma^{\prime}(t)|^{2}=2\bigg{\langle}\frac{D}{dt}\frac{d\gamma}{dt}(t),\frac{d\gamma}{dt}(t)\bigg{\rangle}=0.\nonumber \\ \end{equation}∎