Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
compact oriented Riemannian manifolds
|
| gptkbp:field |
gptkb:algebraic_geometry
differential geometry |
| gptkbp:generalizes |
gptkb:Hodge–de_Rham_spectral_sequence
Kodaira's vanishing theorem |
| https://www.w3.org/2000/01/rdf-schema#label |
Hodge theorem
|
| gptkbp:influenced |
gptkb:Hodge_theory
modern algebraic geometry |
| gptkbp:namedAfter |
gptkb:W._V._D._Hodge
|
| gptkbp:relatedTo |
gptkb:de_Rham_cohomology
harmonic forms |
| gptkbp:state |
On a compact oriented Riemannian manifold, every de Rham cohomology class has a unique harmonic representative.
|
| gptkbp:usedIn |
gptkb:Hodge_decomposition
Kähler manifolds |
| gptkbp:yearProved |
1930s
|
| gptkbp:bfsParent |
gptkb:Riemann_Surfaces
|
| gptkbp:bfsLayer |
8
|