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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 11, Pages 54–66
DOI: https://doi.org/10.26907/0021-3446-2021-11-54-66 (Mi ivm9729) 		 
On the curvatures of a curve in $n$-dimensional Euclidean space

A.M. Shelekhov

Moscow Pedagogical State University, 1 Malaya Pirogovskaya str., bdg. 1, Moscow, 119991 Russia
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DOI: https://doi.org/10.26907/0021-3446-2021-11-54-66
Abstract: Formulas are found for calculating the curvatures of an implicitly defined curve in $n$-dimensional Euclidean space. For these curves, Beltrami's theorem is generalized, which he proved in the three-dimensional case.
Keywords: smooth curve, curvature, implicit definition of a curve, touching $k$-plane of a curve, Beltrami theorem.
Received: 13.01.2021
Revised: 13.01.2021
Accepted: 30.03.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 11, Pages 46–58
DOI: https://doi.org/10.3103/S1066369X21110062
Document Type: Article
UDC: 514.752
Language: Russian
Citation: A.M. Shelekhov, “On the curvatures of a curve in $n$-dimensional Euclidean space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 11, 54–66; Russian Math. (Iz. VUZ), 65:11 (2021), 46–58
Citation in format AMSBIB
\Bibitem{She21}
\by A.M.~Shelekhov
\paper On the curvatures of a curve in $n$-dimensional Euclidean space
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2021
\issue 11
\pages 54--66
\mathnet{http://mi.mathnet.ru/ivm9729}
\crossref{https://doi.org/10.26907/0021-3446-2021-11-54-66}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2021
\vol 65
\issue 11
\pages 46--58
\crossref{https://doi.org/10.3103/S1066369X21110062}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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