Section of a vector bundle
Summary
A section of a vector bundle chooses one vector in the fiber over each point of the base. The choice varies smoothly with the point. Vector fields are sections of the tangent bundle, and differential forms are sections of bundles of alternating forms. The sections of a vector bundle form a vector space, and in fact a module over the ring of smooth functions on the base. Many objects of geometry and physics, such as fields in gauge theory, are sections of suitable bundles.
Where this leads
13 pages build on this one.
- Kuranishi structure
- Hermitian metric on a vector bundle
- Virtual fundamental class
- Lie bracket of vector fields
- Tensor field
- Covariant derivative
- Lyusternik–Fet theorem
- Peetre theorem on local operators
- Differential operator between vector bundles
- Free loop space
- Connection on a vector bundle
- Gromoll–Meyer theorem on closed geodesics
- Manifold of smooth mappings
Further reading
About this page
| Tag | WWX7H5W1RP |
|---|---|
| URI | m2://WWX7H5W1RP |
| Kind | concept |
| Writing | W0 stub |
| MSC | 55R25, 58A05 |
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Used by
- Kuranishi structure
- Hermitian metric on a vector bundle
- Virtual fundamental class
- Lie bracket of vector fields
- Tensor field
- Covariant derivative
- Peetre theorem on local operators
- Differential operator between vector bundles
- Free loop space
- Connection on a vector bundle
- Manifold of smooth mappings