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Classification of (1,1) tensor fields and bihamiltonian structures

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Turiel F. J.

Banach Center Publications

1996

tom 33

nr 1

449-458

Consider a (1,1) tensor field J, defined on a real or complex m-dimensional manifold M, whose Nijenhuis torsion vanishes. Suppose that for each point p ∈ M there exist functions $f_{1},...,f_{m}$, defined around p, such that $(df_{1} ∧ ... ∧ df_{m})(p) ≠ 0$ and $d(df_{j}(J( )))(p) = 0$, j = 1,...,m. Then there exists a dense open set such that we can find coordinates, around each of its points, on which J is written with affine coefficients. This result is obtained by associating to J a bihamiltonian structure on T*M.

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1 Banach Center Publications

1 Turiel F. J.

1 1996

Wyniki wyszukiwania

Classification of (1,1) tensor fields and bihamiltonian structures