Definition:Curve Parametrized by Arc Length
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Definition
Let $\struct {M, g}$ be a Riemannian manifold.
Let $I := \closedint a b$ be a closed real interval.
Let $\gamma : I \to M$ be an admissible unit-speed curve.
Suppose $a = 0$ and $b > 0$.
Then $\gamma$ is said to be parametrized by arc length.
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Definitions