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On some generalization of the construction of twistor spaces. (English) Zbl 0639.53042
Global Riemannian geometry, Proc. Symp., Durham/Engl. 1982, 52-59 (1984).
[For the entire collection see Zbl 0614.00017.]
The authors give a general theory of twistor spaces from the point of view of G-structures. Let $$G\subset GL(2n,R)$$ be a closed subgroup and C a G-invariant set of complex structures in $$R^{2n}$$. If P is a G- structure of an even-dimensional manifold $$M^{2n}$$ then the space $$Z=P\times_ GC$$ amits a natural almost complex structure J depending on a G-connection. The authors prove an integrability theorem for (Z,J) and discuss some examples of this general approach to twistor theory.
Reviewer: Th.Friedrich

MSC:
 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C10 $$G$$-structures