On a synthetic proof of the Ambrose-Palais-Singer theorem for infinitesimally linear spaces

Marta Bunge

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1987)

  • Volume: 28, Issue: 2, page 127-142
  • ISSN: 1245-530X

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Bunge, Marta. "On a synthetic proof of the Ambrose-Palais-Singer theorem for infinitesimally linear spaces." Cahiers de Topologie et Géométrie Différentielle Catégoriques 28.2 (1987): 127-142. <http://eudml.org/doc/91397>.

@article{Bunge1987,
author = {Bunge, Marta},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {geodesics; sprays; manifolds of mappings; infinitesimal linearity; synthetic differential geometry; Ambrose-Palais-Singer Theorem; connections},
language = {eng},
number = {2},
pages = {127-142},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {On a synthetic proof of the Ambrose-Palais-Singer theorem for infinitesimally linear spaces},
url = {http://eudml.org/doc/91397},
volume = {28},
year = {1987},
}

TY - JOUR
AU - Bunge, Marta
TI - On a synthetic proof of the Ambrose-Palais-Singer theorem for infinitesimally linear spaces
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1987
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 28
IS - 2
SP - 127
EP - 142
LA - eng
KW - geodesics; sprays; manifolds of mappings; infinitesimal linearity; synthetic differential geometry; Ambrose-Palais-Singer Theorem; connections
UR - http://eudml.org/doc/91397
ER -

References

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  1. 1, W. Ambrose, R.S. Palais & I.M. Singer, Sprays, Anais da Acad, Bras, de Ciencias, 32-2 (1960). 163-178. Zbl0097.37904MR126234
  2. 2, F. Bergeron, Objets infinitésimalement linéaires dans un modèle bien adapté de G. D.S., in; Géométrie Différenteille Synthétique, Ed, G, E, Reyes, Rapport des recherches DMS 80-12, Univ, Montréal, 1980, 
  3. 3, M. Bunge & E. Dubuc, Local concepts in SDG and germ representability, In: Mathematical Logic and Theoretic Computer Science, Eds, E, G, K, Lopez Escobar & al., Marcel Dekker Inc., New York, 1987, 93-159, Zbl0658.18004MR930679
  4. 4, M. Bunge & M. Heggie, Synthetic Calculus of variations, in: Mathematical applications of Category theory, Ed, J, W, Gray, Contemporary Math, vol, 30, A, M, S, 1984, 30-62, Zbl0582.18006MR749768
  5. 5, M. Bunge & P. Sawyer, On connections, geodesics and sprays in SDG, Cahiers Top, et Géom, Diff, Categ, XXV-3 (1984), 221-257, Zbl0582.18007MR786551
  6. 6, C. Ehresmann, Les prolongements d'une variété différentiable, I, II, III, C, R, A, SParis1951; reprinted in Charles Ehresmann: Oeuvres complètes et commentées, Part I, Amiens, 1984, 
  7. 7, C. Godbillon, Géométrie Différentielle et Mécanique Analytique, Hermann, Paris, 1969, Zbl0174.24602MR242081
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  10. 10, A., Kock, Synthetic Differential Geometry, Cambridge University Press, 1981, Zbl0466.51008MR649622
  11. 11, A. Kock, Remarks on connections and sprays, in: Category theoretic methods in Geometry, Aarhus Math, Inst, Var, Pub, Series 35 (1983), Zbl0552.58001MR739545
  12. 12, A. Kock & R. Lavendhomme, Strong infinitesimal linearity, with applications to strong difference and affine connections, Cahiers Top, et Géom, Diff, Categ, XXV-3 (1984), 311-324, Zbl0564.18009MR786554
  13. 13, S., Maclane, Categories for the working mathematician, Graduate texts in Math, 5, Springer, 1971, Zbl0232.18001MR354798
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  15. 15, F.W. Lawvere, Categorical Dynamics, Aarhus Math, Inst, Var, Pub, Series 30 (1979), 1-29, Zbl0403.18005MR552656
  16. 16, I. Moerdijk & G.E. Reyes, Connections on microlinear spaces, Rapport des recherches, DMS 85-3, Univ, de Montréal (1985), 
  17. 17, I. Moerdijk & G.E. Reyes, On the relation between connections and sprays, Univer, of Amsterdam, Math, Inst, Report 85-18 (1985), 
  18. 18, L.N. Patterson, Connections and prolongations, Can, J Math, XXVII-4 (1975), MR385743
  19. 19, W.A. Poor, Differential geometrie structures, McGraw Hill, 1981, Zbl0493.53027MR647949
  20. 20, B. Veit-Riccioli, Structures on iterated tangent bundles, manuscript, 1981, 
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