Definition:Regular Curve/3-Dimensional Real Vector Space

Definition

Let $\alpha : I \to \R^3$ be a smooth curve.

$\alpha$ is said to be regular if and only if:

$\forall t \in I : \map {\alpha'} t \ne \bszero_{\R^3}$

where:

$\alpha'$ denotes the derivative of $\alpha$

$\bszero_{\R^3}$ denotes the zero vector in $\R^3$

Also see

• Definition:Regular Curve: A more general definition for smooth manifolds

Sources

• 2016: Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces (2nd ed.): $1$-$3$: Regular Curves; Arc Length