Strong infinitesimal linearity, with applications to strong difference and affine connections

A. Kock; R. Lavendhomme

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1984)

  • Volume: 25, Issue: 3, page 311-324
  • ISSN: 1245-530X

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Kock, A., and Lavendhomme, R.. "Strong infinitesimal linearity, with applications to strong difference and affine connections." Cahiers de Topologie et Géométrie Différentielle Catégoriques 25.3 (1984): 311-324. <http://eudml.org/doc/91350>.

@article{Kock1984,
author = {Kock, A., Lavendhomme, R.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {sprays; strong infinitesimal linearity; synthetic differential geometry; affine connections; topos},
language = {eng},
number = {3},
pages = {311-324},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Strong infinitesimal linearity, with applications to strong difference and affine connections},
url = {http://eudml.org/doc/91350},
volume = {25},
year = {1984},
}

TY - JOUR
AU - Kock, A.
AU - Lavendhomme, R.
TI - Strong infinitesimal linearity, with applications to strong difference and affine connections
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1984
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 25
IS - 3
SP - 311
EP - 324
LA - eng
KW - sprays; strong infinitesimal linearity; synthetic differential geometry; affine connections; topos
UR - http://eudml.org/doc/91350
ER -

References

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  1. 1 F. Bergeron, Objet infinitésimalement linéaire dans un modèle adapté de GDS, in: Géométrie Différentielle Synthétique, ed. G. Reyes, Rapport de Recherches. DMS 80-12, Univ. de Montréal: 1980. 
  2. 2 M. Bunge & P. Sawyer, On connections, geodesics and sprays in synthetic differential geometry, Cahiers Top. et Géom. Diff., this issue ; preliminary version in: Category Theoretic Methods in Geometry, Aarhus Var. Publ. Series 35 (1983). Zbl0568.18006MR739541
  3. 3 A. Kock, Properties of well-adapted models for synthetic differential geometry, J. Pure Appl. Algebra20 (1981), 55-70. Zbl0487.18006MR596153
  4. 4 A. Kock, Synthetic differential geometry, London Math. Soc., Lecture Notes Series 51, Cambridge1981. Zbl0466.51008MR649622
  5. 5 A. Kock, Remarks on connections and sprays, in: Category Theoretic Methods in Geometry, Aarhus Var. Publ. Ser. 35 (1983). Zbl0552.58001MR739539
  6. 6 A. Kock & G.E. Reyes, Manifolds in formal differential geometry, in:Applications of Sheaves, Lecture Notes in Math.753, Springer (1979). Zbl0426.14001MR555559
  7. 7 A. Kock & G.E. Reyes, Connections in formal differential, geometry, in: Topos Theoretic Methods in Geometry, Aarhus Var. Publ. Ser. 30 (1979). Zbl0418.18008MR552655
  8. 8 A. Kock, G.E. Reyes & B. Veit, Forms and integration in synthetic differential geometry, Aarhus Preprint Series 31, 1979 -80. Zbl0465.51005MR552662
  9. 9 I. Kolař, Fundamental vector fields on associated fibre bundles, Casopis pro pest. mat.102 (1977), 419-425. Zbl0374.58003MR482887
  10. 10 I. Kolař, On the second tangent bundle and generalized Lie derivatives, Tensor N.S.38 (1982), 98-102. Zbl0512.58002MR832633
  11. 11 R. Lavendhomme, Notes sur l'algèbre de Lie d'un groupe de Lie en geometrie différentielle synthétique, Rapport 111, Inst. de Math., Louvain-La-Neuve (1981). 
  12. 12 P. Libermann, Sur la géométrie des prolongements des espaces fibrés vectoriels, Ann. Inst. Fourier, Grenoble14 (1964), 145-172. Zbl0126.38201MR167925
  13. 13 G.E. Reyes& G.C. Wraith, A note on tangent bundles in a category with a ring object, Math. Scand.42 (1978), 53-63. Zbl0392.18011MR500146
  14. 14 J.E. White, The method of iterated tangents, with applications in local Riemannian geometry, Pitman1982. Zbl0478.58002MR693620

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