Lie Algebroid of a Principal Fibre Bundle

Jan Kubarski

Publications du Département de mathématiques (Lyon) (1989)

  • Issue: 1A, page 1-66
  • ISSN: 0076-1656

How to cite

top

Kubarski, Jan. "Lie Algebroid of a Principal Fibre Bundle." Publications du Département de mathématiques (Lyon) (1989): 1-66. <http://eudml.org/doc/273562>.

@article{Kubarski1989,
author = {Kubarski, Jan},
journal = {Publications du Département de mathématiques (Lyon)},
language = {eng},
number = {1A},
pages = {1-66},
publisher = {Université Claude Bernard - Lyon 1},
title = {Lie Algebroid of a Principal Fibre Bundle},
url = {http://eudml.org/doc/273562},
year = {1989},
}

TY - JOUR
AU - Kubarski, Jan
TI - Lie Algebroid of a Principal Fibre Bundle
JO - Publications du Département de mathématiques (Lyon)
PY - 1989
PB - Université Claude Bernard - Lyon 1
IS - 1A
SP - 1
EP - 66
LA - eng
UR - http://eudml.org/doc/273562
ER -

References

top
  1. [1] M. A. Aragnol, "Sur la geometrie differentielle des espaces fibres", Ann. Sci. Ec. Norm. Sup., (3) 75 (1958), 257-407. Zbl0196.54202MR124002
  2. [2] M. F. Atiyah, "Complex analytic connections in fibre bundles", Trans. A.M.S. Vol.85, No 1, 181-207, 1957. Zbl0078.16002MR86359
  3. [3] C. Ehresmann, "Les connexions infinitesimales dans un espace fibre differentiable", Colloq. Topologie (Bruxelles 1950), Liege1951. Zbl0054.07201MR42768
  4. [4] C. Ehresmann, "Les prolongements d'un espace fibre differentiable", C.R.A.S.Paris, A 240 (1955), 1755-1757. Zbl0064.17502MR71083
  5. [5] W. Greub, S. Halperin, R. Vanstone, "Connections, Curvature, and Cohomology", Vol.II, Academic Press, New York and London, 1973. Zbl0335.57001MR400275
  6. [6] S. Kobayashi, K. Nomizu, "Foundations of differential geometry", Vol.1, Interscience Publishers, New York, London, 1963. Zbl0175.48504MR152974
  7. [7] I. KolaŘ, "Canonical forms on the prolongations of principal fibre bundles", Rev. Roumaine Math. Pures Appl.1971, 16, 1091-1106. Zbl0254.53012MR301668
  8. [8] I. KolaŘ, "Generalized G-Structures and G-Structures of Higher Order", Bollettino U.M.I. (4) 12, Supl. fasc. 3, (1975), 235-256. Zbl0326.53043MR445424
  9. [9] J. Kubarski, "Exponential mapping for Lie groupoids", Coll. Math. Vol. XLVII, 1982, 267-282. Zbl0523.58045MR713145
  10. [10] J. Kubarski, "Exponential mapping for Lie groupoids. Applications", Coll. Math., Vol. LIV, p. 39-48, 1987. Zbl0638.22001MR928656
  11. [11] P. Libermann, "Pseudogroupes infinitesimaux", Coll. Int. CNRS, Lille, 1959, Bull. Soc. Math. France, 87, 1959, 409-425. Zbl0198.26801MR123279
  12. [12] P. Libermann, "Sur les prolongements des fibres principaux et les groupoïdes differentiables", Seminaire Analyse Global, Montreal, 1969. Zbl0248.53031MR356117
  13. [13] P. Libermann, "Parallelismes", Journal of Diff. Geom. Vol. 8, No 4, Dec. 1973, 511-539. Zbl0284.53023MR353189
  14. [14] K. Mackenzie, "Lie Groupoids and Lie Algebroids in Differential Geometry", Cambridge University Press1987, London Mathematical Society, Lecture Note Series124. Zbl0683.53029MR896907
  15. [15] J. Milnor, "On the existence of a connection with curvature zero", Comment. Math. Helv.32 (1958), 215-223. Zbl0196.25101MR95518
  16. [16] P. Molino, "Champs d'elements sur un espace fibre principal differentiable", Ann. Inst. Fourier, Grenoble, 14, 2, (1964) 163-220. Zbl0125.11002MR177367
  17. [17] P. Molino, R. Almeida, "Suites d'Atiyah et feuilletages transversalement complets", C.R.A.S.Paris, t. 300, 13-15, 1985. Zbl0582.57015MR778785
  18. [18] P. Molino, R. Almeida, "Suites d'Atiyah, feuilletages et quantification geometrique", Esctrait du Seminaire du Geometrie Differentielle, Montpellier. Zbl0596.57017
  19. [19] H. K. Nickerson, "On differential operators and connections", Trans A.M.S. Vol.99, 509-539, 1961. Zbl0107.39503MR162212
  20. [20] Ngo-Van-Que, "Du prolongement des espaces fibres et des structures infinitesimales", Ann. Inst. Fourier, Grenoble, 17, 1, 1967, 157-223. Zbl0157.28506MR221416
  21. [21] Ngo-Van-Que, "Sur l'espace de prolongement differentiable", J. of Diff. Geom. Vol. 2, No 1, 1968, 33-40. Zbl0164.22604MR235587
  22. [22] J. Pradines, "Theorie de Lie pour les groupoïdes differentiables, Calcul differential dans la categorie des groupoïdes infinitesimaux", C.R.A.S.Paris, t. 264, 245-248, 1967. Zbl0154.21704MR216409
  23. [23] J. Pradines, "Theorie de Lie pour les groupoïdes differentiables", Atti Conv. Intern. Geom. Diff. Bologna, 1967, Bologna-Amsterdam. Zbl0232.22028
  24. [24] Th. Friedrich, "Zur Abhangigkeit des Dirac-operators Von Der Spin-Struktur", Coll. Math. Vol. XLVIII, Fasc 1, 57-62, 1984. Zbl0542.53026MR750754
  25. [25] J. Milnor, "Spin Structures On Manifolds", L'Enseignement Mathematique (2) 9 (1963), 198-203. Zbl0116.40403MR157388

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.