Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:differential_operator
|
| gptkbp:actsOn |
differential forms
|
| gptkbp:alsoKnownAs |
gptkb:Hodge_Laplacian
|
| gptkbp:defines |
Δ = dδ + δd
|
| gptkbp:domain |
gptkb:Riemannian_manifold
|
| gptkbp:eigenvalues |
related to harmonic forms
|
| gptkbp:field |
gptkb:mathematics
differential geometry |
| gptkbp:generalizes |
gptkb:Laplace–Beltrami_operator
|
| gptkbp:isElliptic |
true
|
| gptkbp:isSelfAdjoint |
true
|
| gptkbp:location |
d is the exterior derivative
δ is the codifferential |
| gptkbp:namedAfter |
gptkb:Georges_de_Rham
gptkb:Pierre-Simon_Laplace |
| gptkbp:notation |
Δ
|
| gptkbp:order |
second order
|
| gptkbp:usedIn |
gptkb:Hodge_theory
gptkb:de_Rham_cohomology |
| gptkbp:bfsParent |
gptkb:Hodge_Laplacian
gptkb:Hodge_star_operator |
| gptkbp:bfsLayer |
7
|
| https://www.w3.org/2000/01/rdf-schema#label |
Laplace–de Rham operator
|