Category:Definitions/Regular Curves

This category contains definitions related to Regular Curves.
Related results can be found in Category:Regular Curves.

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 if and only if:

$\forall t \in I : \map {\gamma'} t \ne 0$