\begin{definition}[Definition:Regular Curve]
Let $M$ be a smooth manifold.
Let $I \subseteq \R$ be a real interval.
Let $\gamma : I \to M$ be a smooth curve.
For all $t \in I$ let $T_{\map \gamma t} M$ be the tangent space of $M$ at the point $\map \gamma t$.
Then $\gamma$ is called a '''regular curve''' iff:
:$\forall t \in I : \map {\gamma'} t \ne 0$
\end{definition}