Complementary 2-forms of Poisson structures

Izu Vaisman

Compositio Mathematica (1996)

  • Volume: 101, Issue: 1, page 55-75
  • ISSN: 0010-437X

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Vaisman, Izu. "Complementary 2-forms of Poisson structures." Compositio Mathematica 101.1 (1996): 55-75. <http://eudml.org/doc/90437>.

@article{Vaisman1996,
author = {Vaisman, Izu},
journal = {Compositio Mathematica},
keywords = {Hamiltonian structure; Poisson manifold; Lie algebroid; Poisson-Nijenhuis structure},
language = {eng},
number = {1},
pages = {55-75},
publisher = {Kluwer Academic Publishers},
title = {Complementary 2-forms of Poisson structures},
url = {http://eudml.org/doc/90437},
volume = {101},
year = {1996},
}

TY - JOUR
AU - Vaisman, Izu
TI - Complementary 2-forms of Poisson structures
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 101
IS - 1
SP - 55
EP - 75
LA - eng
KW - Hamiltonian structure; Poisson manifold; Lie algebroid; Poisson-Nijenhuis structure
UR - http://eudml.org/doc/90437
ER -

References

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  1. 1 Bourbaki, N.: Variétés différentiables et analytiques. Paris, Hermann, 1971. Zbl0217.20401MR281115
  2. 2 Brylinski, J. -L.: A differential complex for Poisson manifolds. J. Diff. Geometry.28 (1988) 93-114. Zbl0634.58029MR950556
  3. 3 Gel'fand, I.M. and Dorfman, I. Ya.: The Schouten bracket and Hamiltonian operators. Funkt. Anal. Prilozhen.14 (3) (1980) 71-74. Zbl0444.58010MR583806
  4. 4 Gel'fand, I.M. and Dorfman, I. Ya.: Hamiltonian operators and the classical Yang-Baxter equation. Funkt. Anal. Prilozhen.16 (4) (1982) 1-9. Zbl0527.58018MR684122
  5. 5 Helgason, S.: Differential Geometry, Lie groups and symmetric spaces. Academic Press, New York, 1978. Zbl0451.53038MR514561
  6. 6 Kosmann-Schwarzbach, Y.: The modified Yang-Baxter equation and bihamiltonian structures. Proc. XVIIth Int. Conf. on Diff. Geom. Methods in Theoretical Physics, Chester1988 (A. Solomon, ed.), World Scientific, Singapore, 1989, 12-25. MR1124411
  7. 7 Kosmann-Schwarzbach, Y. and Magri, F.: Poisson-Nijenhuis structures. Ann. Inst. H. Poincaré, série A (Physique théorique). 53 (1990) 35-81. Zbl0707.58048MR1077465
  8. 8 Koszul, J.L.: Crochet de Schouten-Nijenhuis et cohomologie. In: É. Cartan et les mathématiques d'aujourd'hui. Soc. Math. de France, Astérisque, hors série, 1985, 257-271. Zbl0615.58029MR837203
  9. 9 Libermann, P.: Sur le problème d'équivalence de certaines structures infinitésimales régulières. Ann. Mat. Pura Appl.36 (1954) 27-120. Zbl0056.15401MR66020
  10. 10 Lichnérowicz, A.: Les variétés de Poisson et leurs algèbres de Lie associées. J. Diff. Geometry, 12 (1977) 253-300. Zbl0405.53024MR501133
  11. 11 Mackenzie, K.: Lie groupoids and Lie algebroids in differential geometry. London Math. Soc. Lecture Notes Series124, Cambridge Univ. Press, Cambridge, 1987. Zbl0683.53029MR896907
  12. 12 Magri, F. and Morosi, C.: A geometrical characterization of integrable Hamiltonian Systems through the theory of Poisson- Nijenhuis manifolds. Quaderno S. Univ. of Milan, 19 (1984). 
  13. 13 Thurston, W.P.: Some simple examples of symplectic manifolds. Proc. American Math. Soc.55 (1976) 467-468. Zbl0324.53031MR402764
  14. 14 Vaisman, I.: Cohomology and differential forms. M. Dekker, Inc., New York, 1973. Zbl0267.58001MR341344
  15. 15 Vaisman, I.: Lectures on the geometry of Poisson manifolds. Progress in Math. Series, 118, Birkhäuser, Basel, 1994. Zbl0810.53019MR1269545
  16. 16 Vaisman, I.: The Poisson-Nijenhuis manifolds revisited. Rendiconti Sem. Mat. Torino, 52 (1994). Zbl0852.58042MR1345608
  17. 17 Weil, A.: Introduction à l'étude des variétés Kähleriennes. Hermann, Paris, 1971. Zbl0137.41103
  18. 18 Weinstein, A.: The local structure of Poisson manifolds. J. Diff. Geometry.18 (1983) 523-557. Zbl0524.58011MR723816

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