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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)
Citations:
Zbl 0738.53014
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