Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Riemannian_manifold
vector bundle |
| gptkbp:canBe |
irreducible
reducible |
| gptkbp:class |
gptkb:Berger's_classification
|
| gptkbp:describes |
how vectors are transformed by parallel transport around closed loops
|
| gptkbp:example |
gptkb:Sp(n)
gptkb:G2 gptkb:SO(n) gptkb:SU(n) gptkb:Spin(7) U(n) |
| gptkbp:field |
differential geometry
|
| gptkbp:hasSpecialCase |
restricted holonomy group
|
| https://www.w3.org/2000/01/rdf-schema#label |
holonomy group
|
| gptkbp:importantFor |
gptkb:gauge_theory
gptkb:string_theory theory of symmetric spaces theory of special holonomy |
| gptkbp:introduced |
gptkb:Élie_Cartan
|
| gptkbp:relatedTo |
Levi-Civita connection
affine connection parallel transport connection (mathematics) curvature tensor |
| gptkbp:usedIn |
study of Kähler manifolds
study of Calabi–Yau manifolds study of Einstein manifolds study of Ricci-flat manifolds |
| gptkbp:bfsParent |
gptkb:Riemannian_manifold
|
| gptkbp:bfsLayer |
5
|