Cartan's structure equations
GPTKB entity
Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
connections
differentiable manifolds frame bundles |
| gptkbp:describes |
relationship between connection forms and curvature forms
|
| gptkbp:expressedIn |
gptkb:exterior_calculus
|
| gptkbp:field |
differential geometry
|
| gptkbp:firstEquation |
dθ^i + ω^i_j ∧ θ^j = T^i
|
| gptkbp:formedBy |
gptkb:Élie_Cartan
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cartan's structure equations
|
| gptkbp:namedAfter |
gptkb:Élie_Cartan
|
| gptkbp:publishedIn |
early 20th century
|
| gptkbp:relatedTo |
curvature
torsion |
| gptkbp:secondEquation |
dω^i_j + ω^i_k ∧ ω^k_j = Ω^i_j
|
| gptkbp:usedIn |
gptkb:Riemannian_geometry
theory of connections on manifolds theory of principal bundles |
| gptkbp:bfsParent |
gptkb:Élie_Cartan
|
| gptkbp:bfsLayer |
5
|