Definition:Speed of Smooth Curve

Definition
Let $\struct {M, g}$ be a Riemannian manifold.

Let $I$ be a closed real interval.

Let $\gamma : \R \to M$ be a smooth curve.

Then for any $t \in I$ the speed of $\gamma$ is $\size {\map {\gamma'} t}_g$ where $\size {\, \cdot \,}_g$ is the Riemannian inner product norm.