Riemannian holonomy group

URI: https://gptkb.org/entity/Riemannian_holonomy_group

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept
gptkbp:actsOn	frame bundle tangent bundle
gptkbp:appearsIn	theory of connections theory of symmetric spaces theory of curvature
gptkbp:canBe	gptkb:Sp(n) gptkb:Sp(n)·Sp(1) gptkb:G2 gptkb:SO(n) gptkb:SU(n) gptkb:Spin(7) U(n)
gptkbp:class	gptkb:Berger's_classification
gptkbp:definedIn	parallel transport around loops
gptkbp:determines	parallel transport
gptkbp:field	differential geometry
gptkbp:hasInvariant	gptkb:Riemannian_manifold isometries
gptkbp:heldBy	gptkb:Lie_group
https://www.w3.org/2000/01/rdf-schema#label	Riemannian holonomy group
gptkbp:property	subgroup of orthogonal group
gptkbp:relatedTo	gptkb:holonomy_group gptkb:G2_manifolds gptkb:Ricci-flat_manifolds gptkb:Spin(7)_manifolds gptkb:hyperkähler_manifolds gptkb:quaternion-Kähler_manifolds gptkb:Riemannian_manifold gptkb:Calabi–Yau_manifolds Kähler manifolds
gptkbp:studiedBy	gptkb:Élie_Cartan
gptkbp:studiedIn	gptkb:Riemannian_geometry global differential geometry
gptkbp:usedIn	study of special geometric structures
gptkbp:bfsParent	gptkb:Riemannian_geometry
gptkbp:bfsLayer	5