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Vector fields and generalized vector fields on fibered manifolds

  • II. Differential Geometry
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Geometry and Differential Geometry

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 792))

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References

  1. R. L. Anderson and N. H. Ibragimov, Lie-Bäcklund transformations in applications, SIAM Studies in Applied Mathematics 1, Philadelphia 1979.

    Google Scholar 

  2. R. L. Anderson, S. Kumei and C. E. Wulfman, Generalization of the concept of invariance of differential equations, Phys. Rev. Lett. 28 (1972), 988–991.

    Article  MathSciNet  Google Scholar 

  3. E. Bessel-Hagen, Über die Erhaltungssätze der Elektrodynamik, Math. Ann. 84 (1921), 258–276.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Birkhoff, Hydrodynamics, Princeton University Press, Princeton N. J. 1950 (2nd edition 1960).

    MATH  Google Scholar 

  5. P. R. Chernoff and J. E. Marsden, Properties of infinite dimensional Hamiltonian systems, Lecture Notes in Math. 425, Springer-Verlag, Berlin 1974.

    MATH  Google Scholar 

  6. J. Dieudonné, Cours d'analyse 4, Gauthiers-Villars, Paris 1971.

    Google Scholar 

  7. M. Flato, G. Pinczon and J. Simon, Non linear representations of Lie groups, Ann. sci. Éc. norm. sup. Sér. IV, 10 (1977), 405–418.

    MathSciNet  MATH  Google Scholar 

  8. R. Hermann, E. Cartan's geometric theory of partial differential equations, Advances in Math. 1 (1965), 265–317.

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Hermann, Geometry, Physics and Systems, Marcel Dekker, New York 1973.

    MATH  Google Scholar 

  10. N. H. Ibragimov and R. L. Anderson, Groups of Lie-Bäcklund transformations, Doklady Akad. Nauk SSSR 227 (1976), 539–542 (Soviet Math., Doklady 17 (1976), 437–441).

    MathSciNet  MATH  Google Scholar 

  11. H. H. Johnson, Bracket and exponential for a new type of vector field, Proc. Amer. math. Soc. 15 (1964), 432–437.

    Article  MathSciNet  MATH  Google Scholar 

  12. _____, A new type of vector field and invariant differential systems, 675–678.

    Article  MathSciNet  MATH  Google Scholar 

  13. A. A. Kirillov, Local Lie algebras, Uspehi mat. Nauk 31 (1976), 57–76 (Russ. math. Surveys 31 (1976), 55–75).

    MathSciNet  MATH  Google Scholar 

  14. I. Kolář, Fundamental vector fields on associated vector bundles, Časopis Pěst. Mat. 102 (1977), 419–425.

    MATH  Google Scholar 

  15. Y. Kosmann, On Lie transformation groups and the covariance of differential operators, Differential Geometry and Relativity, M. Cahen and M. Flato eds., Reidel, Dordrecht 1976.

    Google Scholar 

  16. Y. Kosmann-Schwarzbach, Sur les transformations de similitude des équations aux dérivées partielles, C. r. Acad. Sci., Paris, 287 Sér. A (1978), 953–956.

    MathSciNet  MATH  Google Scholar 

  17. _____, Dérivées de Lie des morphismes de fibrés, Publ. math. Univ. Paris VII, 3 (1978), 55–72.

    MathSciNet  Google Scholar 

  18. _____, Infinitesimal conditions for the equivariance of morphisms of fibered manifolds, Proc. Amer. math. Soc. 77 (1979), 374–380.

    Article  MathSciNet  MATH  Google Scholar 

  19. _____, Generalized symmetries of nonlinear partial differential equations, Lett. math. Phys. 3 (1979), 395–404.

    Article  MathSciNet  MATH  Google Scholar 

  20. _____, The vertical bracket and its applications to symmetries and Bäcklund transformations, to appear.

    Google Scholar 

  21. N. Kuiper and K. Yano, On geometric objects and Lie groups of transformations, Nederl. Akad. Wet., Proc., Ser. A 58 (1955), 411–420.

    MathSciNet  MATH  Google Scholar 

  22. S. Kumei, Invariance transformations, invariance group transformations, and invariance groups of the sine-Gordon equations, J. math. Phys. 16 (1975), 2461–2468.

    Article  MathSciNet  Google Scholar 

  23. B. A. Kupershmidt, On the geometry of jet manifolds, Uspehi mat. Nauk 30 (1975), 211–212.

    MathSciNet  Google Scholar 

  24. _____, Geometry of jet bundles and the structure of Lagrangian and Hamiltonian formalisms, preprint (1979).

    Google Scholar 

  25. P. D. Lax, Integrals of nonlinear equations of evolution and solitary waves, Comm. pure appl. Math. 21 (1968), 467–490.

    Article  MathSciNet  MATH  Google Scholar 

  26. P. Lecomte, Sur l'algèbre de Lie des automorphismes infinitésimaux du fibré tangent, C. r. Acad. Sci., Paris, 288 Sér. A (1979), 661–663.

    MathSciNet  MATH  Google Scholar 

  27. A. Lichnerowicz, Géométrie des groupes de transformations, Dunod, Paris 1958.

    MATH  Google Scholar 

  28. S. Lie, Gesammelte Abhandlungen, vol. 3, Teubner, Leipzig 1922.

    Google Scholar 

  29. F. Magri, An operator approach to Poisson brackets, Ann. of Phys. 99 (1976), 196–228.

    Article  MathSciNet  MATH  Google Scholar 

  30. _____, An operator approach to symmetries, Nuovo Cimento 34 B (1976), 334–344.

    Article  MathSciNet  Google Scholar 

  31. W. Miller, Jr., Lie theory and special functions, Academic Press, New York 1968.

    MATH  Google Scholar 

  32. K. Nomizu, Lie groups and differential geometry, Math. Soc. Japan, 1956.

    Google Scholar 

  33. P. J. Olver, Symmetry groups and conservation laws in the formal variational calculus, preprint (1978).

    Google Scholar 

  34. R. S. Palais, Banach manifolds of fiber bundle sections, Actes Congrès Intern. Math. (Nice 1970), vol. 2, Gauthiers-Villars, Paris 1971, 243–249.

    MATH  Google Scholar 

  35. _____, Foundations of global non-linear analysis, Benjamin, New York 1968.

    MATH  Google Scholar 

  36. S. Salvioli, On the theory of geometric objects, J. diff. Geometry 7 (1972), 257–278.

    MathSciNet  MATH  Google Scholar 

  37. K. Shiga, Cohomology of Lie algebras over a manifold, I, J. math. Soc. Japan 26 (1974), 324–361.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics Brooklyn College, City University of New York, 11210, Brooklyn, N.Y.

    Yvette Kosmann-Schwarzbach

Authors
  1. Yvette Kosmann-Schwarzbach
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Rafael Artzy Izu Vaisman

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© 1980 Springer-Verlag

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Kosmann-Schwarzbach, Y. (1980). Vector fields and generalized vector fields on fibered manifolds. In: Artzy, R., Vaisman, I. (eds) Geometry and Differential Geometry. Lecture Notes in Mathematics, vol 792. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088687

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  • DOI: https://doi.org/10.1007/BFb0088687

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09976-5

  • Online ISBN: 978-3-540-39214-9

  • eBook Packages: Springer Book Archive

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