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- Calabi_conjecture abstract "In mathematics, the Calabi conjecture was a conjecture about the existence of certain "nice" Riemannian metrics on certain complex manifolds, made by Eugenio Calabi (1954, 1957) and proved by Shing-Tung Yau (1977, 1978). Yau received the Fields Medal in 1982 in part for this proof. The Calabi conjecture states that a compact Kähler manifold has a unique Kähler metric in the same class whose Ricci form is any given by 2-form representing the first Chern class. In particular if the first Chern class vanishes there is a unique Kähler metric in the same class with vanishing Ricci curvature; these are called Calabi–Yau manifolds.More formally, the Calabi conjecture states:If M is a compact Kähler manifold with Kähler metric and Kähler form , and R is any (1,1)-form representing the manifold's first Chern class, then there exists a unique Kähler metric on M with Kähler form such that and represent the same class in cohomology H2(M,R) and the Ricci form of is R.The Calabi conjecture is closely related to the question of which Kähler manifolds have Kähler–Einstein metrics.".
- Calabi_conjecture wikiPageExternalLink books?id=n_ZQAAAAMAAJ.
- Calabi_conjecture wikiPageExternalLink ICM1954.2.
- Calabi_conjecture wikiPageExternalLink icm1954.2.0206.0207.ocr.pdf.
- Calabi_conjecture wikiPageExternalLink 1798.
- Calabi_conjecture wikiPageExternalLink Calabi-Yau_manifold.
- Calabi_conjecture wikiPageExternalLink k6w204w55607k5t2.
- Calabi_conjecture wikiPageID "5263012".
- Calabi_conjecture wikiPageRevisionID "580028198".
- Calabi_conjecture authorlink "Eugenio Calabi".
- Calabi_conjecture authorlink "Shing-Tung Yau".
- Calabi_conjecture first "Eugenio".
- Calabi_conjecture first "Shing-Tung".
- Calabi_conjecture hasPhotoCollection Calabi_conjecture.
- Calabi_conjecture last "Calabi".
- Calabi_conjecture last "Yau".
- Calabi_conjecture year "1954".
- Calabi_conjecture year "1957".
- Calabi_conjecture year "1977".
- Calabi_conjecture year "1978".
- Calabi_conjecture subject Category:Complex_manifolds.
- Calabi_conjecture subject Category:Differential_geometry.
- Calabi_conjecture type Artifact100021939.
- Calabi_conjecture type ComplexManifolds.
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- Calabi_conjecture type Manifold103717750.
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- Calabi_conjecture comment "In mathematics, the Calabi conjecture was a conjecture about the existence of certain "nice" Riemannian metrics on certain complex manifolds, made by Eugenio Calabi (1954, 1957) and proved by Shing-Tung Yau (1977, 1978). Yau received the Fields Medal in 1982 in part for this proof. The Calabi conjecture states that a compact Kähler manifold has a unique Kähler metric in the same class whose Ricci form is any given by 2-form representing the first Chern class.".
- Calabi_conjecture label "Calabi conjecture".
- Calabi_conjecture label "カラビ予想".
- Calabi_conjecture sameAs カラビ予想.
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- Calabi_conjecture wasDerivedFrom Calabi_conjecture?oldid=580028198.
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