Global analysis, analysis on manifolds Concept
Differential form
Summary
A differential form is an object that one can integrate over curves, surfaces, volumes and their higher-dimensional analogues. A -form assigns to each point an alternating -linear function of tangent vectors. Forms give a coordinate-free approach to multivariable calculus.
Where this leads
56 pages build on this one.
- One-form
- Wedge product of forms
- Exterior derivative
- Closed and exact forms
- Index of the de Rham complex
- Hodge star operator
- Lichnerowicz formula
- Kohn–Rossi cohomology
- Moser's trick
- Elliptic complex
- Hodge theorem
- Almgren–Pitts min-max theory
- Signature operator
- Spin(7)-manifold
- Exterior differential system
- Symplectic manifold
- Weitzenböck identity
- Lichnerowicz vanishing theorem
- Iwasawa manifold
- Yau–Tian–Donaldson conjecture
- Pfaffian system
- Chern–Simons theory
- Contact structure on a jet bundle
- Hermitian manifold
- Hodge Laplacian
- Connection on a principal bundle
- Finite element exterior calculus
- Hodge decomposition
- Principal symbol of an operator on a manifold
- de Rham theorem
- Area-minimizing current
- Dolbeault operator
- (p,q)-form
- Dbar operator
- Lagrangian submanifold
- G2 manifold
- Symplectomorphism
- Cartan's magic formula
- Differential operator between vector bundles
- Hilbert's invariant integral
- Haar measure on a Lie group
- Tautological one-form
- Abelian differential
- Period map
- Elliptic operator on a compact manifold
- Hamiltonian vector field
- de Rham cohomology
- Calabi conjecture
- Contact manifold
- Maurer–Cartan form
- Frölicher–Nijenhuis bracket
- Hodge conjecture
- Kähler manifold
- Curvature form
- Chern–Simons form
- Current
Further reading
- Web https://en.wikipedia.org/wiki/Differential_form, lead section
About this page
| Tag | 0E3G0GRPZ6 |
|---|---|
| URI | m2://0E3G0GRPZ6 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 58A10 |
| Same as |
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What this page needs for W2
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- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Special cases
Used by
- One-form
- Wedge product of forms
- Exterior derivative
- Closed and exact forms
- Hodge star operator
- Kohn–Rossi cohomology
- Hodge theorem
- Signature operator
- Spin(7)-manifold
- Exterior differential system
- Symplectic manifold
- Weitzenböck identity
- Pfaffian system
- Chern–Simons theory
- Contact structure on a jet bundle
- Hermitian manifold
- Hodge Laplacian
- Connection on a principal bundle
- Finite element exterior calculus
- de Rham theorem
- Area-minimizing current
- Dolbeault operator
- (p,q)-form
- Lagrangian submanifold
- G2 manifold
- Symplectomorphism
- Cartan's magic formula
- Haar measure on a Lie group
- Tautological one-form
- Abelian differential
- Hamiltonian vector field
- de Rham cohomology
- Contact manifold
- Frölicher–Nijenhuis bracket
- Kähler manifold
- Chern–Simons form
- Current