The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature

Ngaiming Mok

Type: Article

Publication Date: 1988-01-01

Citations: 256

DOI: https://doi.org/10.4310/jdg/1214441778

Abstract

Soit (X, h) une variete de Kahler compacte a n dimensions de courbure bisectionnelle holomorphe non negative et soit (X~, h~) son espace de recouvrement universel. Alors il existe des entiers non negatifs k, N 1 ,…, N l et des espaces symetriques hermitiens compacts ineductibles M 1 ,…, M k de rang ≥2, tels que (X~, h~) est isometriquement bi-holomorphe a (C k , g 0 )×(P Nu 1, θ 1 )×…×(P Nu l, θ l )×(M 1 , g 1 )×…×(M p , g p ), ou g 0 est la metrique euclidienne sur C k , g 1 ,…, g p sont des metriques canoniques sur M 1 , …, M p , et θ i , 1≤i≤l, est une metrique de Kahler sur P Nu i portant une courbure bisectionnelle holomorphe non negative

Locations

Journal of Differential Geometry - View - PDF

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