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gptkbp:instanceOf
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gptkb:algebraic_geometry
gptkb:mathematical_concept
gptkb:topology
gptkb:Riemannian_manifold
homogeneous space
symmetric space
surface of revolution
compact surface
Lie group homogeneous space
real algebraic surface
simply connected surface
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gptkbp:antipodalMap
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involution
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gptkbp:area
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4π
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gptkbp:borders
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none
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gptkbp:canBeDescribedByEquation
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x^2 + y^2 + z^2 = 1
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gptkbp:canBeEmbeddedIn
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Euclidean 3-space
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gptkbp:canBeStereographicallyProjectedTo
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gptkb:aircraft
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gptkbp:compact
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true
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gptkbp:dimensions
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2
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gptkbp:Euler_characteristic
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2
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gptkbp:fundamentalGroup
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trivial group
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gptkbp:genus
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0
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gptkbp:hasConnection
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true
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gptkbp:hasSpecialCase
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n-sphere
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gptkbp:homologyGroup
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H_2 = Z
H_0 = Z
H_1 = 0
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gptkbp:homotopyGroup
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π_1 = 0
π_2 = Z
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https://www.w3.org/2000/01/rdf-schema#label
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2-sphere (S^2)
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gptkbp:includesMetric
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round metric
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gptkbp:isBoundaryless
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true
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gptkbp:isClosedManifold
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true
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gptkbp:isCompactManifold
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true
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gptkbp:isomorphicTo
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complex projective line
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gptkbp:isOrientableManifold
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true
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gptkbp:isSmoothManifold
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true
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gptkbp:orientable
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true
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gptkbp:symmetry
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O(3)
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gptkbp:universalCover
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gptkb:real_projective_plane
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gptkbp:usedIn
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gptkb:geometry
gptkb:topology
complex analysis
differential geometry
physics
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gptkbp:volumeEnclosed
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4/3 π
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gptkbp:bfsParent
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gptkb:Riemann_sphere
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gptkbp:bfsLayer
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6
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