Definition:Normal Space/Manifold
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Definition
Let $\struct {\tilde M, \tilde g}$ be a Riemannian manifold.
Let $M \subseteq \tilde M$ be a smooth submanifold with or without boundary in $\tilde M$.
Let $p \in M$ be a point in $M$.
Suppose $v$ is normal to $M$ at $p$.
The set of all such $v$ at $p$ is called the normal space (of $M$ at $p$) and is denoted by $N_p M = \paren {T_p M}^\perp$
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Methods for Constructing Riemannian Metrics