Definition:Unit-Speed Curve
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Definition
Let $\struct {M, g}$ be a Riemannian manifold.
Let $I$ be a closed real interval.
Let $\gamma : \R \to M$ be a smooth curve.
Suppose the speed of $\gamma$ is equal to $1$:
- $\size {\map {\gamma'} t}_g = 1$
where $\size {\, \cdot \,}_g$ is the Riemannian inner product norm.
Then $\gamma$ is a unit-speed curve.
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Definitions