Year: 1994
Type: preprint
Abstract: Let Z be a compact complex (2n+1)-manifold which carries a {\em complex contact structure}, meaning a codimension-1 holomorphic sub-bundle D of 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^{4n}, g). If Z also admits a second complex contact structure, then Z= CP_{2n+1}. As an application, we give several new characterizations of the Riemannian manifold HP_n=Sp(n+1)/( Sp(n)\times Sp(1)).
Source: arXiv (Cornell University)
Author: LeBrun, Claude
Institution: Stony Brook University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952828745