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

• Autorzy: Francisco Javier Turiel
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

(1,1) tensor field; bihamiltonian structure

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 33
• Numer: 1
• Strony: 449-458

Daty

wydano

1996

Twórcy

autor

Francisco Javier Turiel

• Sección de Matemáticas, Facultad de Ciencias, A.P. 59, 29080 Málaga, Spain

Bibliografia

• [1] R. Brouzet, P. Molino et F. J. Turiel, Géométrie des systèmes bihamiltoniens, Indag. Math. 4 (3) (1993), 269-296.
• [2] P. Cabau, J. Grifone et M. Mehdi, Existence de lois de conservation dans le cas cyclique, Ann. Inst. H. Poincaré Phys. Théor. 55 (1991), 789-803.
• [3] A. Frölicher and A. Nijenhuis, Theory of vector-valued differential forms, Part I, Indag. Math. 18 (1956), 338-359.
• [4] J. Grifone and M. Mehdi, Existence of conservation laws and characterization of recursion operators for completely integrable systems, preprint, Univ. Toulouse II, 1993.
• [5] J. Lehmann-Lejeune, Intégrabilité des G-structures définies par une 1-forme 0-déformable à valeurs dans le fibré tangent, Ann. Inst. Fourier (Grenoble) 16 (1966), 329-387.
• [6] H. Osborn, The existence of conservation laws, I, Ann. of Math. 69 (1959), 105-118.
• [7] H. Osborn, Les lois de conservation, Ann. Inst. Fourier (Grenoble) 14 (1964), 71-82.
• [8] F. J. Turiel, Structures bihamiltoniennes sur le fibré cotangent, C. R. Acad. Sci. Paris Sér. I 308 (1992), 1085-1088.
• [9] F. J. Turiel, Classification locale simultanée de deux formes symplectiques compatibles, Manuscripta Math. 82 (1994), 349-362.