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

Banach Center Publications (1996)

- Volume: 33, Issue: 1, page 449-458
- ISSN: 0137-6934

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topTuriel, Francisco. "Classification of (1,1) tensor fields and bihamiltonian structures." Banach Center Publications 33.1 (1996): 449-458. <http://eudml.org/doc/262671>.

@article{Turiel1996,

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.},

author = {Turiel, Francisco},

journal = {Banach Center Publications},

keywords = {(1,1) tensor field; bihamiltonian structure; Nijenhuis torsion; bi-Hamiltonian structure},

language = {eng},

number = {1},

pages = {449-458},

title = {Classification of (1,1) tensor fields and bihamiltonian structures},

url = {http://eudml.org/doc/262671},

volume = {33},

year = {1996},

}

TY - JOUR

AU - Turiel, Francisco

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

JO - Banach Center Publications

PY - 1996

VL - 33

IS - 1

SP - 449

EP - 458

AB - 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.

LA - eng

KW - (1,1) tensor field; bihamiltonian structure; Nijenhuis torsion; bi-Hamiltonian structure

UR - http://eudml.org/doc/262671

ER -

## References

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- [3] A. Frölicher and A. Nijenhuis, Theory of vector-valued differential forms, Part I, Indag. Math. 18 (1956), 338-359.
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- [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. Zbl0145.42103
- [6] H. Osborn, The existence of conservation laws, I, Ann. of Math. 69 (1959), 105-118. Zbl0119.07801
- [7] H. Osborn, Les lois de conservation, Ann. Inst. Fourier (Grenoble) 14 (1964), 71-82. Zbl0126.10904
- [8] F. J. Turiel, Structures bihamiltoniennes sur le fibré cotangent, C. R. Acad. Sci. Paris Sér. I 308 (1992), 1085-1088. Zbl0767.57013
- [9] F. J. Turiel, Classification locale simultanée de deux formes symplectiques compatibles, Manuscripta Math. 82 (1994), 349-362.

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