## 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

### MSC:

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

### Keywords:

almost product structure; polynomial structure

Zbl 0326.53050