Statements (93)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:item
|
| gptkbp:can_be_used_to |
compactify extra dimensions
|
| gptkbp:constructed_in |
toric varieties
|
| gptkbp:dimensions |
complex dimension 3
|
| gptkbp:has_applications_in |
gptkb:Physics
algebraic geometry |
| gptkbp:has_property |
Ricci-flat metric
holomorphic forms |
| gptkbp:has_topology |
non-trivial fundamental group
|
| https://www.w3.org/2000/01/rdf-schema#label |
Calabi Yau Manifold
|
| gptkbp:is_a |
gptkb:topology
gptkb:architecture gptkb:Kähler_manifold Riemannian manifold complex manifold geometric structure symplectic manifold projective variety complex algebraic variety differential geometry object differentiable manifold Calabi-Yau variety Kähler-Einstein manifold complex differential geometry object complex geometry object complex manifold with trivial canonical bundle non-singular variety algebraic geometry object complex manifold structure differential topology object holomorphic manifold |
| gptkbp:is_aligned_with |
conformal symmetry
|
| gptkbp:is_associated_with |
gptkb:superstring_theory
string compactification |
| gptkbp:is_characterized_by |
Ricci-flat metric
special holonomy Kähler metric vanishing first Chern class holomorphic volume form holomorphic sections holonomy group SU(n) Calabi-Yau condition holomorphic vector bundles vanishing of the Ricci curvature Kähler structure vanishing second Chern class |
| gptkbp:is_connected_to |
gptkb:topology
gptkb:F-theory string compactification moduli space Calabi-Yau compactification Calabi-Yau manifolds in mathematics Calabi-Yau manifolds in physics |
| gptkbp:is_related_to |
gptkb:F-theory
gptkb:Calabi_conjecture Hodge theory mirror symmetry topological string theory string theory models string theory landscape string landscape string theory compactification Calabi-Yau metrics Calabi-Yau theorem string theory research topics |
| gptkbp:is_studied_in |
algebraic geometry
differential geometry mathematical physics mathematical analysis theoretical mathematics geometric analysis string theory research theoretical physics research mathematical physics literature mathematical physics research |
| gptkbp:is_used_in |
gptkb:quantum_field_theory
gptkb:heterotic_string_theory gptkb:Physics gptkb:string_theory gptkb:M-theory gptkb:superstring_theory mathematical modeling compactification quantum gravity research mathematical physics applications mathematical physics research string duality mathematical physics theories |
| gptkbp:length |
gptkb:6
complex dimension 3 |
| gptkbp:named_after |
gptkb:Eugenio_Calabi
|
| gptkbp:related_to |
mirror symmetry
|
| gptkbp:used_in |
gptkb:string_theory
|