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gptkbp:instanceOf
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gptkb:mathematical_concept
Complex manifold
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gptkbp:compact
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Yes
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gptkbp:connectedTo
|
Yes
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gptkbp:definedIn
|
Quotient of complex vector space by lattice
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gptkbp:dimensions
|
n (for n-dimensional complex torus)
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gptkbp:first_Betti_number
|
2n
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gptkbp:fundamentalGroup
|
Lattice Λ
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gptkbp:has_translation-invariant_metric
|
Yes
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gptkbp:has_universal_cover
|
C^n
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gptkbp:hasSpecialCase
|
Elliptic curve (for n=1)
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|
https://www.w3.org/2000/01/rdf-schema#label
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Complex torus
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gptkbp:is_a_commutative_group
|
Yes
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gptkbp:is_a_complex_analytic_group
|
Yes
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gptkbp:is_a_complex_Lie_group
|
Yes
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gptkbp:is_a_complex_manifold_of_dimension_n
|
Yes
|
|
gptkbp:is_a_complex_parallelizable_manifold
|
Yes
|
|
gptkbp:is_a_group_variety
|
Yes
|
|
gptkbp:is_a_homogeneous_space
|
Yes
|
|
gptkbp:is_a_Kähler_manifold
|
Yes
|
|
gptkbp:is_a_parallelizable_manifold
|
Yes
|
|
gptkbp:is_a_principal_homogeneous_space
|
Yes
|
|
gptkbp:is_a_quotient_space
|
Yes
|
|
gptkbp:is_an_abelian_variety
|
If it is projective
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|
gptkbp:isQuotientOf
|
C^n / Λ (Λ is a lattice in C^n)
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gptkbp:structure
|
gptkb:group_of_people
Complex Lie group
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|
gptkbp:used_in
|
gptkb:Algebraic_geometry
gptkb:Differential_geometry
Complex analysis
|
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gptkbp:bfsParent
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gptkb:Abelian_varieties
|
|
gptkbp:bfsLayer
|
7
|