\begin{definition}[Definition:Backward Reparametrization of Curve]
Let $M$ be a smooth manifold.
Let $I, I' \subseteq \R$ be real intervals.
Let $\gamma : I \to M$ be a smooth curve.
Let $\phi : I' \to I$ be a diffeomorphism.
Let $\tilde \gamma$ be a curve defined by:
:$\tilde \gamma := \gamma \circ \phi : I' \to M$
where $\circ$ denotes the composition of mappings $\gamma$ and $\phi$.
Suppose $\phi$ is decreasing.
Then $\tilde \gamma$ is called the '''backward reparametrization of $\gamma$'''.
\end{definition}