Complete Kähler–Einstein metrics under certain holomorphic covering and Examples  [ Métriques complètes de Kähler–Einstein sous certains revêtements holomorphes et exemples ]
Annales de l'Institut Fourier, à paraître, 21 p.

Nous établissons l’unique métrique complète de Kähler–Einstein avec courbure scalaire négative sur une large classe de variétés de Kähler complètes, y compris les variétés dont l’espace de recouvrement peut être biholomorphiquement plongé dans une variété de Kähler à courbure sectionnelle holomorphe limitée au-dessus par une constante négative. Nous présentons en outre plusieurs nouveaux exemples de variétés complètes de Kähler–Einstein non compactes, générés par les résultats.

We establish the unique complete Kähler–Einstein metric with negative scalar curvature on a broad class of complete Kähler manifolds, including those manifolds whose covering space can be biholomorphically embedded into a Kähler manifold with holomorphic sectional curvature bounded above by a negative constant. We further present several new examples of complete noncompact Kähler–Einstein manifolds, generated by the results.

Publié le : 2019-03-08
Classification:  32Q15,  32Q20,  53C55,  32H02
Mots clés: Métrique de Kähler–Einstein, revêtements holomorphes, variétés complètes de Kähler, exemples
@unpublished{AIF_0__0_0_A38_0,
     author = {Wu, Damin and Yau, Shing--Tung},
     title = {Complete K\"ahler--Einstein metrics under certain holomorphic covering and Examples},
     note = {to appear in \emph{Annales de l'Institut Fourier}},
}
Wu, Damin; Yau, Shing–Tung. Complete Kähler–Einstein metrics under certain holomorphic covering and Examples. Annales de l'Institut Fourier, à paraître, 21 p.

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