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Metric of special \(2F\)-flat Riemannian spaces. (English) Zbl 1089.53020

The notion of \(F\)-planar mapping was introduced by J. Mikeš and N. S. Sinyukov [Izv. Vyssh. Uchebn. Zaved., Mat. 1983, No. 1(248), 55–61 (1983; Zbl 0514.53008)]. In this paper the author considers a \(2F\)-flat Riemannian space \(V_n\), that is a Riemannian space endowed with an affinor structure \(F\) such that \(F^3= I\), which is \(2F\)-planar mapped on flat space. He determines explicitly the metric tensor \(g\) of that Riemannian space \(V_n\).

MSC:

53B20 Local Riemannian geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53B35 Local differential geometry of Hermitian and Kählerian structures
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)

Citations:

Zbl 0514.53008
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References:

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