Definition:Admissible Loop

Definition

Let $M$ be a smooth manifold.

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

Let $\gamma : I \to M$ be a curve segment.

Let $\gamma$ be an admissible curve.

Let $p \in M$.

Suppose $\map \gamma a = \map \gamma b = p$.

Then $\gamma$ is called the admissible loop (based at point $p$).

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 5$: The Levi-Civita Connection. Problems