Definition:Complete Disconnected Riemannian Manifold

Definition

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

Suppose $M$ is geodesically complete or that every disconnected component is a complete metric space.

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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