Definition:Admissible Subdivision for Admissible Curve

Definition

Let $M$ be a smooth manifold.

Let $I := \closedint a b$ be a closed real interval.

Let $\gamma : I \to M$ be an admissible curve.

Let $\tuple {x_0, x_1, x_2, \ldots, x_{n - 1}, x_n}$ be a finite subdivision of $I$.

Then $\tuple {x_0, x_1, x_2, \ldots, x_{n - 1}, x_n}$ is said to be an admissible subdivision for $\gamma$.

Sources

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