On the twistor space of pseudo-spheres
Abstract
We give a new proof that the sphere S6 does not admit an integrable orthogonal complex structure, as in LeBrun, following the methods from twistor theory. We present the twistor space of a pseudo-sphere S2n2q=SO2p+1,2q/SO2p,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.
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