Abstract
An important problem in differential geometry is how one can compare tangent vectors at one point to those at another, at least in the case of nearby points. We ask if, at least during an infinitesimal period of time, it is possible to “transport” a tangent vector in the direction of another tangent vector.
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KOCK, A., and REYES, G.E., Connections in formal differential geometry, in [1979], 158–195.
KOCK, A., and LAVENDHOMME, R., Strong infinitesimal linearity, with applications to strong difference and affine connections, Cahiers Top. Geom. diff. 25 (1984), 311–324.
BUNGE, M., and SAWYER, P., On connections, geodesics and sprays in synthetic differential geometry,Cahier Top. Géom. Diff., 25 (1984), 221–258 (preprinted in ([26])).
KOCK, A.,(ed), Category theoretic Methods in Geometry, edited by A.Kock, Various Publications Series n35, Aarhus, 1983.
MOERDIJK, I., and REYES, G.E., Models for Smooth Infinitesimal Analysis, Springer, 1991.
LAVENDHOMME, R., Leçons de Géométrie Différentielle Synthétique Naïve, Monographies de mathématiques 3, Ciaco, Louvain-laneuve, (1987), 204 pp.
KOCK, A., A combinatorial theory of connections, Contemporary Mathematics, AMS, 30 (1984), 132–144.
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© 1996 Springer Science+Business Media Dordrecht
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Lavendhomme, R. (1996). Connections. In: Basic Concepts of Synthetic Differential Geometry. Kluwer Texts in the Mathematical Sciences, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4588-7_5
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DOI: https://doi.org/10.1007/978-1-4757-4588-7_5
Publisher Name: Springer, Boston, MA
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