Symmetries of connections on fibered manifolds

Alexandr Vondra

Archivum Mathematicum (1994)

  • Volume: 030, Issue: 2, page 97-115
  • ISSN: 0044-8753

Abstract

top
The (infinitesimal) symmetries of first and second-order partial differential equations represented by connections on fibered manifolds are studied within the framework of certain “strong horizontal“ structures closely related to the equations in question. The classification and global description of the symmetries is presented by means of some natural compatible structures, eġḃy vertical prolongations of connections.

How to cite

top

Vondra, Alexandr. "Symmetries of connections on fibered manifolds." Archivum Mathematicum 030.2 (1994): 97-115. <http://eudml.org/doc/247563>.

@article{Vondra1994,
abstract = {The (infinitesimal) symmetries of first and second-order partial differential equations represented by connections on fibered manifolds are studied within the framework of certain “strong horizontal“ structures closely related to the equations in question. The classification and global description of the symmetries is presented by means of some natural compatible structures, eġḃy vertical prolongations of connections.},
author = {Vondra, Alexandr},
journal = {Archivum Mathematicum},
keywords = {connections; differential equations; integral sections; symmetries; differential equations for integral sections of connections; strong horizontal distributions; symmetries},
language = {eng},
number = {2},
pages = {97-115},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Symmetries of connections on fibered manifolds},
url = {http://eudml.org/doc/247563},
volume = {030},
year = {1994},
}

TY - JOUR
AU - Vondra, Alexandr
TI - Symmetries of connections on fibered manifolds
JO - Archivum Mathematicum
PY - 1994
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 030
IS - 2
SP - 97
EP - 115
AB - The (infinitesimal) symmetries of first and second-order partial differential equations represented by connections on fibered manifolds are studied within the framework of certain “strong horizontal“ structures closely related to the equations in question. The classification and global description of the symmetries is presented by means of some natural compatible structures, eġḃy vertical prolongations of connections.
LA - eng
KW - connections; differential equations; integral sections; symmetries; differential equations for integral sections of connections; strong horizontal distributions; symmetries
UR - http://eudml.org/doc/247563
ER -

References

top
  1. Fundamental ideas and concepts of differential geometry, Itogi nauki i tekhniki, Sovremennye problemy matematiki 28, “VINITI", Moscow, 1988. (Russian) (1988) MR1315326
  2. Non-holonomic connections, Liet. matem. rink. 27(1) (1987), 15–27. (Russian) (1987) MR0895955
  3. Methods of Differential Geometry in Analytical Mechanics, North-Holland Mathematics Studies 158, North-Holland, Amsterdam, 1989. (1989) MR1021489
  4. Time-dependent linear Lagrangians: the inverse problem, symmetries and constants of motion, preprint, 1992. 
  5. On certain natural transformations between connections, Proc. Conf. Diff. Geom. and Its Appl., Opava 1992, Silesian Univ., Opava, 1992, pp. 273–279. (1992) MR1255548
  6. Symmetries of Distributions and Quadrature of Ordinary Differential Equations, preprint, 1991. MR1128153
  7. Some natural operations with connections, J. Nat. Acad. Math. 5 (1987), 127–141. (1987) MR0994555
  8. Connections in 2-fibered manifolds, Arch. Math. (Brno) 17 (1981), 23–30. (1981) MR0672485
  9. Natural Operations in Differential Geometry, Springer, 1993. (1993) MR1202431
  10. Prolongations of vector fields to jet bundles, In Proc. of the Winter School on Geometry and Physics, Srní, 1989, Suppl. Rendiconti Circolo Mat. Palermo, Serie II 21, 1989, pp. 103–111. (1989) 
  11. Some geometrical aspects of variational problems on fibered manifolds, Folia Fac. Sci. Nat. Univ. Purk. Brun. Phys. XIV (1973), 1–65. (1973) 
  12. Lectures on differential invariants, Folia Fac. Sci. Nat. Univ. Purk. Brun. Phys., J. E. Purkyně University, Brno, 1990. (1990) MR1108622
  13. Hamilton-Jacobi distributions, preprint, 1989. 
  14. Variational analysis on fibered manifolds over one-dimensional bases, Ph.D. Thesis, Dept. of Mathematics, Silesian Univ. at Opava, Czechoslovakia, 1992. 
  15. On some integration methods for connections on fibered manifolds, Proc. Conf. Diff. Geom. and Its Appl., Opava 1992, Silesian Univ., Opava, 1992, pp. 89–101. (1992) MR1255531
  16. Fibred spaces, Jet spaces and Connections for Field Theories, In Proceedings of International Meeting “Geometry and Physics", Florence, 1982, Pitagora Editrice, Bologna, 1983, pp. 135–165. (1983) MR0760841
  17. Connections and differential calculus on fibred manifolds. Applications to field theory, Istituto di Matematica Applicata “G.Sansone", Firense (to appear). (to appear) 
  18. Jet involution and prolongation of connections, Časopis Pěst. Mat. 114(4) (1989), 356–365. (1989) MR1027231
  19. Applications of Lie groups to differential equations, Translation to Russian, “Mir", Moscow, 1989, Springer-Verlag, 1986. (1986) Zbl0588.22001MR0836734
  20. Toward a classification of dynamical symmetries in classical mechanics, Bull. Austral. Math. Soc. 27 (1983), 53–71. (1983) Zbl0495.58014MR0696644
  21. A complete classification of dynamical symmetries in classical mechanics, Bull. Austral. Math. Soc. 32 (1985), 299–308. (1985) Zbl0578.58018MR0815371
  22. Adjoint symmetries of second-order differential equations and generalizations, In Proc. Conf. Diff. Geom. and Its Appl., Brno, 1989, World Scientific, Singapore, 1990, pp. 412–421. (1990) Zbl0787.58018MR1062048
  23. Calculus of forms along a map adapted to the study of second-order differential equations, preprint, 1992. MR1255533
  24. The Geometry of Jet Bundles, London Mathematical Society Lecture Note Series 142, Cambridge University Press, Cambridge, 1989. (1989) Zbl0665.58002MR0989588
  25. An introduction to the geometry of nonlinear differential equations, “Nauka", Moscow, 1986. (Russian) (1986) MR0855844
  26. On some connections related to the geometry of regular higher–order dynamics, (to appear). (to appear) 
  27. Sprays and homogeneous connections on R × T M , Arch. Math. (Brno) 28 (1992), 163–173. (1992) Zbl0790.53028MR1222283
  28. The contravariant theory of the differential prolongation on a space with a connection, Itogi nauki i tekhniki, Problemy geometrii (14), “VINITI", Moscow, 1983, pp. 101–176. (Russian) (1983) MR0697391
  29. The 1-integrability of non-holonomic differential geometrical structures. 1. Γ 1 , 2 - connections, Liet. matem. rink. 27(1) (1987), 28–37. (Russian) (1987) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.