On the twistor space of pseudo-spheres

Details On the twistor space of pseudo-spheres On the twistor space of pseudo-spheres

2005-09-20

arxiv.org/abs/math/0509442v2

Differential Geometry and its Applications, 25 (2007), pp. 207-219

Mathematics

Differential Geometry

Added the MSC's hoping Arxiv will "run" a better distribuition through Subj-class's. The article has 20 pages

Scientific paper

10.1016/j.difgeo.2006.08.004

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.

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