\begin{definition}[Definition:Curve Parametrized by Arc Length]
Let $\struct {M, g}$ be a Riemannian manifold.
Let $I := \closedint a b$ be a closed real interval.
Let $\gamma : I \to M$ be an admissible unit-speed curve.
Suppose $a = 0$ and $b > 0$.
Then $\gamma$ is said to be '''parametrized by arc length'''.
\end{definition}