Category:Tubular Neighborhoods
This category contains results about Tubular Neighborhoods.
Definitions specific to this category can be found in Definitions/Tubular Neighborhoods.
Smooth Manifold
Definition:Tubular Neighborhood of Smooth Manifold
Embedded Riemannian Submanifold
Let $\struct {M, g}$ be a Riemannian manifold.
Let $P \subseteq M$ be an embedded submanifold.
Let $\pi : NP \to P$ be the normal bundle of $P$ in $M$.
Let $\EE$ be the domain of the exponential map.
Let $\EE_P = \EE \cap NP$.
Let $U \subseteq M$, $V \subseteq \EE_P$ be open subsets.
Let $E$ be the normal exponential map.
Suppose $U$ is the normal neighborhood of $P$ in $M$.
Let $\delta : P \to \R$ be a positive continuous function.
Suppose $U$ is the diffeomorphic image under $E$ of $V$ where:
- $V = \set {\tuple {x, v} \in NP : \norm v_g < \map \delta x}$
Then $U$ is called the tubular neighborhood of $P$ in $M$.
Pages in category "Tubular Neighborhoods"
The following 2 pages are in this category, out of 2 total.