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Particular \(F\)-structure on vector bundle and compatible \(D\)-connections. (English) Zbl 0978.53046
Let the dimension of the total space \(E\) be \(n+m\), \(\dim T_H(E) = n\), \(\dim T_V(E) = m\). A tensor field \(f\) of type \({{1\;1}\choose{1\;1}}\) is considered for which \(f^3 + f = 0\). The connection \(\bigtriangledown\) compatible with \(f\) is defined. Using different adapted bases the \(f\) structures of first and second kind are defined and the components of the \(d\)-connection \(\bigtriangledown\) are determined.
MSC:
53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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