On the twistor space of pseudo-spheres |
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Authors: | R Albuquerque IMC Salavessa |
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Institution: | a Universidade de Évora, Rua Romão Ramalho, 59, 7000 Évora, Portugal b Instituto Superior Técnico, Edifício Ciência, Piso 3, 1049-001 Lisboa, Portugal |
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Abstract: | We give a proof that the sphere S6 does not admit an integrable orthogonal complex structure using simple differential geometric methods. This appears as a corollary of a general analogous result concerning pseudo-spheres.We study the twistor space of a pseudo-Riemannian manifold in both the holomorphic and pseudo-Riemannian directions. In particular, we construct the twistor space of a pseudo-sphere as a known pseudo-Kähler symmetric space. This leads to the explicit, unexpected computation of the exterior derivative of the Kähler form on the base manifold. |
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Keywords: | primary 32H02 32L25 53B30 53B35 secondary 32C15 53C28 32Q10 32Q15 |
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