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Manifold with the structure satisfying \(F^{k+1}-a^ 2 F^{k-1}=0\). (English) Zbl 0885.53029

The author considers a non-null tensor field \(F\) of type (1,1) and of class \(C^\infty\) on an \(n\)-dimensional connected differentiable manifold \(M^n\) of class \(C^\infty\) such that \(F^{k+1}- a^2F^{k-1} =0\) \((k\in \mathbb{N}\), a constant), \(\text{rank} (F)= {1\over 2} (\text{rank} F^{k-1} +\dim M^n) =\text{constant} r\).
He associates to \(F\) some operators and proves some identities concerning such operators. He also establishes some integrability conditions for the structure \(F\).
Reviewer: N.L.Youssef (Giza)

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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