Uniform Tubular Neighborhood Theorem

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