# FANO MANIFOLDS, CONTACT STRUCTURES, AND QUATERNIONIC GEOMETRY

@article{Lebrun1994FANOMC, title={FANO MANIFOLDS, CONTACT STRUCTURES, AND QUATERNIONIC GEOMETRY}, author={Claude Lebrun}, journal={International Journal of Mathematics}, year={1994}, volume={06}, pages={419-437} }

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 Kahler-Einstein metric of positive scalar curvature, we show that it is the Salamon twistor space of a quaternion-Kahler manifold (M4n, g). If Z also admits a second complex contact structure , then Z=CP2n+1. As an application, we give several new characterizations of the Riemannian manifold HPn= Sp(n+1)/(Sp(n…

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