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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2021 Number 11, Pages 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

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.

UDC: 514.752

Received: 13.01.2021
Revised: 13.01.2021
Accepted: 30.03.2021

DOI: 10.26907/0021-3446-2021-11-54-66


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, 65:11, 46–58


© Steklov Math. Inst. of RAS, 2025