Classification of (1,1) tensor fields and bihamiltonian structures
Volume 33 / 1996
Banach Center Publications 33 (1996), 449-458
DOI: 10.4064/-33-1-449-458
Abstract
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.
