Definition:Uniform Tubular Neighborhood
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Definition
Let $\struct {M, g}$ be a Riemannian manifold.
Let $P \subseteq M$ be an embedded submanifold.
Let $U \subseteq M$ be the tubular neighborhood of $P$ in $M$ with $\map \delta x = \epsilon$ where $\epsilon \in \R_{> 0}$.
Then $U$ is called the uniform tubular neighborhood (or $\epsilon$-tubular neighborhood) of $P$ in $M$.
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 5$: The Levi-Civita Connection. Tubular Neighborhoods and Fermi Coordinates