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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.)
##### Keywords:
$$f$$-structure; vector bundle; connection
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