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Proceedings of the London Mathematical Society Advance Access originally published online on February 20, 2008
Proceedings of the London Mathematical Society 2008 96(3):738-766; doi:10.1112/plms/pdm035
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© 2008 London Mathematical Society

Twistors and 3-symmetric spaces

Jean-Baptiste Butruille

LATP, Université de Provence
39, rue Frédéric Joliot-Curie
13453 Marseille cedex 13
France

Received 26 April 2006.

We describe complex twistor spaces over inner 3-symmetric spaces G/H, such that H acts transitively on the fibre. As in the symmetric case, the complex twistor spaces are flag manifolds G/K, where K is the centralizer of a torus in G. Moreover, they carry an almost complex structure defined using the horizontal distribution of the normal connection on G/H that coincides with the complex structure associated to a parabolic subgroup PsubGC if it is integrable. Conversely, starting from a complex flag manifold GC/P, there exists a natural fibration with complex fibres on a 3-symmetric space, called fibration of degree 3.

2000 Mathematics Subject Classification 22E60, 53C10, 53C28, 53C30.


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