Abstract
Using the classical Elie Cartan method, we construct a canonical frame for a smooth curve in multidimensional affine space with canonical and non-canonical parameters.
Similar content being viewed by others
References
Blaschke, W. Introduction to Geometry of Webs (Fizmatgiz, Moscow, 1959) [Russian translation].
Shirokov, P. A., Shirokov, A. P. Affine Differential Geometry (Fizmatgiz, Moscow, 1959) [in Russian].
Davis, D. Generic Affine Differential Geometry of Curves in Rn, Proc. Royal Soc. Edinburgh 136A, 1195–1205 (2006).
Favard, J. Course de Gémétrie Différentialle Locale (Gauthier-Villars, Paris, 1957; Moscow, 1960).
Izumiya, S., Sano, T. Generic Affine Differential Geometry of Plane Curves, Proc. Royal Soc. Edinburgh 128A, 301–314 (1998).
Izumiya, S., Sano, T. Generic Affine Differential Geometry of Space Curves, Proc. Edinburgh Math. Soc. 41, 315–324 (1998).
Evtushik, L. E., Lumiste, Yu. G., Ostianu, N. M., Shirokov, A. P. Differential-Geometric Structures on Manifolds, J. Sov. Math. 14, 1573–1719 (1980).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.I. Kabanova, A.M. Shelekhov, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 4, pp. 23–31.
About this article
Cite this article
Kabanova, M.I., Shelekhov, A.M. Canonical frames of a curve in multidimensional affine space. Russ Math. 60, 17–24 (2016). https://doi.org/10.3103/S1066369X16040046
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X16040046