Geodesic
Symmetric matrices and maximal Nijenhuis pencils
Sbornik. Mathematics, Tome 214 (2023) no. 8, pp. 1101-1110 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Nijenhuis pencil is a linear subspace of the space of $(1,1)$ tensor field which consists of Nijenhuis operators. The problem of the description of maximal (by inclusion) Nijenhuis pencils containing a subpencil of dimension $n(n+1)/2$ such that the operators in it are — in some system of coordinates — constant symmetric matrices, is solved. Two such pencils turn out to exist, both of which arise in a natural way in applications, for example, in the theory of infinite-dimensional integrable systems. Bibliography: 6 titles.
Keywords: geometry, Frölicher-Nijenhuis bracket, Nijenhuis pencils. 
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A. Yu. Konyaev. Symmetric matrices and maximal Nijenhuis pencils. Sbornik. Mathematics, Tome 214 (2023) no. 8, pp. 1101-1110. http://geodesic.mathdoc.fr/item/SM_2023_214_8_a2/

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