On the twistor space of pseudo-spheres
arXiv:math/0509442 · doi:10.1016/j.difgeo.2006.08.004
Abstract
We give a new proof that the sphere S^6 does not admit an integrable orthogonal complex structure, as in \cite{LeBrun}, following the methods from twistor theory. We present the twistor space of a pseudo-sphere S^{2n}_{2q}=SO_{2p+1,2q}/SO_{2p,2q} as a pseudo-Kähler symmetric space. We then consider orthogonal complex structures on the pseudo-sphere, only to prove such a structure cannot exist.
Added the MSC's hoping Arxiv will "run" a better distribuition through Subj-class's. The article has 20 pages