|
gptkbp:instanceOf
|
gptkb:mathematical_concept
gptkb:topology
gptkb:Riemannian_manifold
|
|
gptkbp:compact
|
true
|
|
gptkbp:constructedAs
|
product of n circles
|
|
gptkbp:dimensions
|
n
|
|
gptkbp:fundamentalGroup
|
Z^n
|
|
gptkbp:hasConnection
|
true
|
|
gptkbp:hasFlatMetric
|
true
|
|
gptkbp:hasSpecialCase
|
2-dimensional torus (n=2)
circle (n=1)
|
|
gptkbp:homologyGroup
|
direct sum of binomial(n,k) copies of Z in degree k
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
n-dimensional torus
|
|
gptkbp:isAbelianLieGroup
|
true
|
|
gptkbp:isClosedManifold
|
true
|
|
gptkbp:isCompactLieGroup
|
true
|
|
gptkbp:isComplexManifold
|
true
|
|
gptkbp:isConnectedLieGroup
|
true
|
|
gptkbp:isFlatManifold
|
true
|
|
gptkbp:isGroupManifold
|
true
|
|
gptkbp:isGroupObject
|
true
|
|
gptkbp:isHausdorff
|
true
|
|
gptkbp:isHomogeneousManifold
|
true
|
|
gptkbp:isHomogeneousSpace
|
true
|
|
gptkbp:isKählerManifold
|
true
|
|
gptkbp:isLocallyEuclidean
|
true
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isNonAbelian
|
true
|
|
gptkbp:isOrientable
|
true
|
|
gptkbp:isParallelizable
|
true
|
|
gptkbp:isParallelizableManifold
|
true
|
|
gptkbp:isPathConnected
|
true
|
|
gptkbp:isProductManifold
|
true
|
|
gptkbp:isQuotientOf
|
R^n by Z^n
|
|
gptkbp:isRiemannianManifold
|
true
|
|
gptkbp:isSecondCountable
|
true
|
|
gptkbp:isSmoothManifold
|
true
|
|
gptkbp:isSymplecticManifold
|
true
|
|
gptkbp:notation
|
(S^1)^n
T^n
|
|
gptkbp:universalCover
|
R^n
|
|
gptkbp:usedIn
|
gptkb:geometry
gptkb:topology
dynamical systems
physics
|
|
gptkbp:bfsParent
|
gptkb:Lie_group
|
|
gptkbp:bfsLayer
|
5
|