On some generalization of the construction of twistor spaces. (English) Zbl 0639.53042

Bérard Bergery, Lionel; Ochiai, T.

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

Keywords:

twistor spaces; G-structures; complex structures; almost complex structure; integrability theorem