A Class of Nonpositively Curved Kähler Manifolds Biholomorphic to the Unit Ball in C
نویسندگان
چکیده
Let (M, g) be a simply connected complete Kähler manifold with nonpositive sectional curvature. Assume that g has constant negative holomorphic sectional curvature outside a compact set. We prove that M is then biholomorphic to the unit ball in Cn, where dimCM = n. Résumé. Soit (M, g) une variété kählérienne complète et simplement connexe à courbure sectionnelle non-positive. Supposons que g ait courbure sectionnelle holomorphe constante et négative en delors d’un compact. On démontre que M est biholomorphe à une boule dans C, où dimCM = n.
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