Definition:Complete Connected Riemannian Manifold

Definition

Let $\struct {M, g}$ be a connected Riemannian manifold.

Suppose $M$ is geodesically complete or metrically complete.

Then $M$ is said to be complete.

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 6$: Geodesics and Distance. Completeness