Uniform Tubular Neighborhood Theorem
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Theorem
Let $\struct {M, g}$ be a Riemannian manifold.
Let $S$ be a submanifold of $M$.
Suppose $S$ is compact.
Then $S$ has a uniform tubular neighborhood in $M$.
Proof
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Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 5$: The Levi-Civita Connection. Tubular Neighborhoods and Fermi Coordinates