On the twistor space of pseudo-spheres
  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-K\"ahler symmetric space. We then consider orthogonal complex structures on the pseudo-sphere, only to prove such a structure cannot exist. 
R. Albuquerque and Isabel M.C. Salavessa