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gptkbp:instanceOf
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gptkb:mathematical_concept
Kähler manifold
Ricci-flat manifold
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gptkbp:dimensions
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arbitrary (commonly 3)
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gptkbp:example
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gptkb:butter
gptkb:K3_surface
gptkb:quintic_threefold
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gptkbp:field
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gptkb:algebraic_geometry
gptkb:theoretical_physics
differential geometry
complex geometry
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gptkbp:firstDefined
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1970s
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https://www.w3.org/2000/01/rdf-schema#label
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Calabi–Yau manifolds
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gptkbp:importantFor
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gptkb:algebraic_geometry
gptkb:string_theory
gptkb:mirror_symmetry
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gptkbp:namedAfter
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gptkb:Eugenio_Calabi
gptkb:Shing-Tung_Yau
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gptkbp:property
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vanishing first Chern class
admit a Ricci-flat Kähler metric
admit covariantly constant spinors
admit nowhere vanishing holomorphic n-form
holonomy group is a subgroup of SU(n)
simply connected (in many cases)
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gptkbp:provenBy
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gptkb:Shing-Tung_Yau
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gptkbp:relatedTo
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gptkb:string_theory
gptkb:F-theory
gptkb:D-branes
gptkb:M-theory
gptkb:topological_string_theory
gptkb:Batyrev's_construction
gptkb:Calabi_conjecture
gptkb:Donaldson–Thomas_invariants
gptkb:Gromov–Witten_invariants
gptkb:Strominger–Yau–Zaslow_conjecture
gptkb:topological_field_theory
moduli space
toric geometry
string compactification
string landscape
Hodge numbers
holonomy group SU(n)
monodromy
mirror pairs
vacuum solutions in string theory
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gptkbp:usedIn
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compactification in string theory
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gptkbp:bfsParent
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gptkb:string_theory
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gptkbp:bfsLayer
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5
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