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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

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