Oubiña, J. A.; Gadea, P. M. On the existence of J(4,2)-structures. (English) Zbl 0555.53018 Riv. Mat. Univ. Parma, IV. Ser. 9, 179-184 (1983). A J(4,2)-structure on a \(C^{\infty}\)-manifold V of dimension \(n=2k\) is a \(C^{\infty}\) (1,1)-tensor field J on V satisfying i) \(J^ 4+J^ 2=0\) and ii) rank J\(=(rank J^ 2+n)/2\). If J is of constant rank V is called J(4,2)-manifold. The operators \(l=-J^ 2\) and \(m=J^ 2+1\) are projectors of the almost product structure on V. Denote by L and M the corresponding distributions. We have \(TV=L+M\). This decomposition is used for proofs of some properties of characteristic classes (Pontjagin classes, Stiefel-Whitney classes and the Euler class in the orientable case) of a J(4,2)-manifold, establishing obstructions to the existence of a J(4,2)-structure on a given manifold. Reviewer: J.Bureš MSC: 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) Keywords:J(4,2)-structure; almost product structure; characteristic classes PDFBibTeX XMLCite \textit{J. A. Oubiña} and \textit{P. M. Gadea}, Riv. Mat. Univ. Parma, IV. Ser. 9, 179--184 (1983; Zbl 0555.53018)