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On almost complex structures on fibre bundles. (English) Zbl 0856.53026
Let $$\varphi$$ be an almost contact structure on a manifold $$M$$. J. Janyška [Arch. Math., Brno 26, No. 4, 229-239 (1990; Zbl 0738.53014)] proved that there is no connection that is canonically induced by an almost complex structure $$\varphi$$ on $$M$$. In this paper, the author considers a fibre bundle $$\pi:Y\to M$$, where the dimension of fibres equals $$\dim M$$, and studies natural operators transforming tensor fields $$\varphi$$ of type (1,1) on $$Y$$ into connections on $$Y$$. In particular, such connections are constructed when $$\varphi$$ is an almost complex structure.
##### MSC:
 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 58A20 Jets in global analysis 53C05 Connections (general theory)
Zbl 0738.53014