Natural transformations in differential geometry

Gerd Kainz; Peter W. Michor

Czechoslovak Mathematical Journal (1987)

  • Volume: 37, Issue: 4, page 584-607
  • ISSN: 0011-4642

How to cite


Kainz, Gerd, and Michor, Peter W.. "Natural transformations in differential geometry." Czechoslovak Mathematical Journal 37.4 (1987): 584-607. <>.

author = {Kainz, Gerd, Michor, Peter W.},
journal = {Czechoslovak Mathematical Journal},
keywords = {product-preserving functor; Weil algebra; Lie brackets; covariant differentiation},
language = {eng},
number = {4},
pages = {584-607},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Natural transformations in differential geometry},
url = {},
volume = {37},
year = {1987},

AU - Kainz, Gerd
AU - Michor, Peter W.
TI - Natural transformations in differential geometry
JO - Czechoslovak Mathematical Journal
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 37
IS - 4
SP - 584
EP - 607
LA - eng
KW - product-preserving functor; Weil algebra; Lie brackets; covariant differentiation
UR -
ER -


  1. H. Federer, Geometric measure theory, Grundlehren Band 153, Springer Verlag 1969. (1969) Zbl0176.00801MR0257325
  2. D. B. A. Epstein W. P. Thurston, Transformation groups and natural bundles, Proc. London Math. Soc. (III), 38 (1979), 219-236. (1979) Zbl0409.58001MR0531161
  3. A. Kock, Synthetic differential geometry, London Math. Society, Lecture Note Series 51, 1981. (1981) Zbl0487.18006MR0649622
  4. I. Kolář, Natural transformations of the second tangent functor into itself, Arch. Math. (Brno) 4, 1984. (1984) Zbl0578.58004MR0784868
  5. A. Kriegl, 10.1007/BF01301929, Monatshefte Math. 94 (1982), 109-124. (1982) MR0678046DOI10.1007/BF01301929
  6. I. Moerdijk K. E. Reyes, The tangent functor category revisited, Preprint, Amsterdam 1983. (1983) Zbl0623.58002
  7. I. Moerdijk С. E. Reyes, C -rings, Preprint Montréal 1984. (1984) 
  8. В. L. Reinhart, Differential geometry of foliations, Ergebnisse 99, Springer-Verlag 1983. (1983) Zbl0506.53018MR0705126
  9. I. Rosický, Abstract tangent functors, Preprint Brno 1984. (1984) Zbl0561.18008MR0800500
  10. S. Šwierczkowski, A description of the tangent functor category, Coll. Math. 31 (1974). (1974) Zbl0302.58002MR0379628
  11. С. L. Terng, Natural vector bundles and natural differential operators, Amer. J. Math. 100, 775-828. Zbl0422.58001MR0509074
  12. A. Vanžurová, On geometry of the third tangent bundle, Acta Univ. Olom. 82 (1985). (1985) Zbl0619.53013MR0879025
  13. A. Weil, Théorie des points proches sur les variétés differentiables, in Colloq. Top et Geo. Diff., Strassbourg 1953, 111-117. (1953) Zbl0053.24903MR0061455
  14. J. E. White, The method of iterated tangents with applications in local Riemannian geometry, Pitman 1982. (1982) Zbl0478.58002MR0693620
  15. David J. Eck, Product preserving functors on smooth manifolds, preprint 1985. (1985) Zbl0606.58006MR0857563
  16. O. O. Luciano, Categories of multiplicative functors and Morimoto's Conjecture, Preprint 1986. (1986) 

Citations in EuDML Documents

  1. Włodzimierz M. Mikulski, Product preserving bundle functors on fibered manifolds
  2. Włodzimierz M. Mikulski, Fiber product preserving bundle functors as modified vertical Weil functors
  3. Ivan Kolar, An abstract characterization of the jet spaces
  4. Włodzimierz M. Mikulski, There exists a prolongation functor of infinite order
  5. Ivan Kolář, Covariant approach to natural transformations of Weil functors
  6. Piotr Kobak, Natural liftings of vector fields to tangent bundles of bundles of 1 -forms
  7. Jacek Dębecki, Some liftings of Poisson structures to Weil bundles
  8. Andreas Kriegl, Peter W. Michor, Product preserving functors of infinite-dimensional manifolds
  9. Ivan Kolář, Gabriela Vosmanská, Natural transformations of higher order tangent bundles and jet spaces
  10. Ivan Kolář, Zbigniew Radziszewski, Natural transformations of second tangent and cotangent functors

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