Fano Manifolds, Contact Structures, and Quaternionic Geometry
نویسنده
چکیده
Let Z be a compact complex (2n+1)-manifold which carries a complex contact structure, meaning a codimension-1 holomorphic sub-bundle D ⊂ TZ which is maximally non-integrable. If Z admits a Kähler-Einstein metric of positive scalar curvature, we show that it is the Salamon twistor space of a quaternion-Kähler manifold (M, g). If Z also admits a second complex contact structure D̃ 6= D, then Z = CP2n+1. As an application, we give several new characterizations of the Riemannian manifold HPn = Sp(n + 1)/ (Sp(n) × Sp(1)).
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تاریخ انتشار 1995