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.
KeywordsVector Bundle Basic Concept Covariant Derivative Tangent Vector Fibre Bundle
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- KOCK, A., and REYES, G.E., Connections in formal differential geometry, in , 158–195.Google Scholar
- BUNGE, M., and SAWYER, P., On connections, geodesics and sprays in synthetic differential geometry,Cahier Top. Géom. Diff., 25 (1984), 221–258 (preprinted in ()).Google Scholar
- KOCK, A.,(ed), Category theoretic Methods in Geometry, edited by A.Kock, Various Publications Series n35, Aarhus, 1983.Google Scholar
- MOERDIJK, I., and REYES, G.E., Models for Smooth Infinitesimal Analysis, Springer, 1991.Google Scholar