Definition:Parametrized Curve

Definition

Let $M$ be a smooth manifold.

Let $I \subseteq \R$ be a real interval.

The parametrized curve, denoted by $\gamma$, is a continuous mapping such that:

$\gamma : I \to M$

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Lengths and Distances