Definition:Complete Disconnected Riemannian Manifold
Jump to navigation
Jump to search
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.
![]() | This article needs to be linked to other articles. In particular: Disconnected component or equivalent You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding these links. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{MissingLinks}} from the code. |
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