Global analysis, analysis on manifolds Concept
Tangent bundle
Summary
The tangent bundle of a smooth manifold collects all tangent vectors at all points into one space. A point of the tangent bundle is a pair: a point of the manifold and a velocity vector at that point. The tangent bundle is itself a smooth manifold of twice the dimension, and it is the basic example of a vector bundle. Vector fields are its sections, and the derivative of a smooth map is a map between tangent bundles.
Where this leads
37 pages build on this one.
- Riemannian metric
- Exponential map
- Vector fields on spheres
- Differential of a smooth map
- Frobenius theorem
- Frame bundle
- Spectral decomposition theorem
- Lie bracket of vector fields
- Pseudo-Riemannian manifold
- Smale–Hirsch theorem
- CR manifold
- Tensor field
- Infinitesimal stability
- Moving frame
- Pfaffian system
- Affine connection
- Whitney stratification
- Hermitian manifold
- Tubular neighborhood theorem
- Sub-Riemannian manifold
- Tangential Cauchy–Riemann equations
- Finsler manifold
- Almost complex manifold
- Hyperbolic set
- Killing vector field
- Axiom A
- Foliation
- Kodaira–Spencer map
- Connection on a vector bundle
- Newlander–Nirenberg theorem
- Slice theorem
- Ehresmann connection
- Contact manifold
- Anosov diffeomorphism
- Cartan–Kähler theorem
- Stability conjecture
- Parallelizable manifold
Further reading
About this page
| Tag | WY6K3P4YCG |
|---|---|
| URI | m2://WY6K3P4YCG |
| Kind | concept |
| Writing | W0 stub |
| MSC | 58A05, 57R22 |
| Specializes | Fiber bundle |
| Same as |
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Used by
- Riemannian metric
- Exponential map
- Vector fields on spheres
- Differential of a smooth map
- Frobenius theorem
- Frame bundle
- Lie bracket of vector fields
- Pseudo-Riemannian manifold
- Smale–Hirsch theorem
- CR manifold
- Tensor field
- Infinitesimal stability
- Moving frame
- Affine connection
- Whitney stratification
- Tubular neighborhood theorem
- Sub-Riemannian manifold
- Tangential Cauchy–Riemann equations
- Finsler manifold
- Almost complex manifold
- Killing vector field
- Foliation
- Kodaira–Spencer map
- Connection on a vector bundle
- Ehresmann connection
- Parallelizable manifold