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.