\begin{definition}[Definition:Riemannian Length of Admissible Curve]
Let $\struct {M, g}$ be a Riemannian manifold.
Let $\closedint a b$ be a closed real interval.
Let $\gamma : \closedint a b \to M$ be an admissible curve.
Then the '''(Riemannian) length of $\gamma$''', denoted by $\map {L_g} \gamma$, is defined by:
:$\ds \map {L_g} \gamma := \int_a^b \size {\map \gamma t}_g \rd t$
where $\size {\map \gamma t}_g$ is the Riemannian inner product norm.
\end{definition}