Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appearsIn |
decomposition of the Riemann curvature tensor
study of conformal invariants |
| gptkbp:component |
gptkb:Ricci_tensor
metric tensor scalar curvature |
| gptkbp:defines |
A symmetric 2-tensor constructed from the Ricci tensor and scalar curvature
|
| gptkbp:dimensions |
defined for n > 2
|
| gptkbp:field |
differential geometry
|
| gptkbp:form |
P_{ij} = (1/(n-2))(R_{ij} - (1/2(n-1))R g_{ij})
|
| gptkbp:hasInvariant |
conformal transformations (up to a certain transformation law)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Schouten tensor
|
| gptkbp:namedAfter |
gptkb:Jan_Arnoldus_Schouten
|
| gptkbp:rank |
(0,2) tensor
|
| gptkbp:relatedTo |
gptkb:Weyl_tensor
gptkb:Ricci_tensor gptkb:Riemann_curvature_tensor |
| gptkbp:symbol |
P
|
| gptkbp:usedIn |
gptkb:Riemannian_geometry
gptkb:conformal_geometry |
| gptkbp:bfsParent |
gptkb:Weyl_tensor
gptkb:Differential_geometry |
| gptkbp:bfsLayer |
5
|