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The normal addition map for a Euclidean submanifold
Definition
Let be an embedded smooth submanifold. Using the Euclidean inner product, define its orthogonal normal bundle by Local slice charts and orthogonal projection onto give this set its standard smooth rank- vector-bundle structure. The normal addition map is It restricts on the zero section to the inclusion and is the basic model map used to build Euclidean tubular neighbourhoods.
Depends on
Used by
- De rham cohomology is continuous homotopy invariant on smooth manifolds Corollary
- A noncompact embedded curve with no uniform tubular radius Example
- Immersion extension on a disk: absolute and relative parametric forms Lemma
- Normal addition is a local diffeomorphism along the zero section Lemma
- Smoothing continuous families of genuine immersions Lemma
- Variable-radius injectivity for normal addition Lemma
- Strong Whitney approximation by transverse maps Theorem
- The Euclidean tubular neighbourhood theorem Theorem
- The tubular neighbourhood theorem in a smooth ambient manifold Theorem
- Whitney approximation for manifold-valued maps Theorem
Dependency tree · two levels
30 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- John M. Lee, Introduction to Smooth Manifolds, 2nd ed., Tubular Neighborhoods (standard reference, not scraped)