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On a structure satisfying \(F^ k -(-1)^{k+1} F=0\). (English) Zbl 0845.53023

Let \(M^n\) be a differentiable manifold and \(F\) a non-null tensor field of type (1,1) and of constant rank \(r\), defined on \(M^n\) and satisfying the relation: \(F^k- (- 1)^{k+ 1} F= 0\), where \(k\) is a fixed positive integer greater than 2. The author gives some results on the structure defined on \(M^n\) by the tensor field \(F\).

MSC:

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