Almost product and almost complex structures generated by polynomial structures. (English) Zbl 0582.53032

The author investigates a tensor field f of type (1,1) on a differentiable manifold M satisfying the equation \(P(f)=0\), where \(P(z)=a_ 0(x)z^ n+a_ 1(x)z^{n-1}+...+a_ n(x)\) is a polynomial over the ring \(C^{\infty}(M)\). She proves that under some additional assumptions about the polynomial P a tensor field f satisfying \(P(f)=0\) induces on M an almost product structure and a polynomial structure J satisfying \(J^ 3+J=0\). These results represent a generalization of results of the reviewer [Kodai Math. Semin. Rep. 27, 42-50 (1976; Zbl 0326.53050)].
Reviewer: J.Vanzura


53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
15B57 Hermitian, skew-Hermitian, and related matrices


Zbl 0326.53050