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On the Curvatures of a Curve in n-Dimensional Euclidean Space

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Abstract

Formulas are obtained for calculating the curvatures of an implicitly defined curve in n-dimensional Euclidean space. For these curves, Beltrami's theorem is generalized, which was proved by Beltrami in the case of three-dimensional space.

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REFERENCES

  1. Jordan C. "Sur la théorie des courbes dans l'espace à n dimensions", in: Oeuvres, Vol. 4, 337-339 (Gauthier-Villars, et Blanchard, Paris, 1964).

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  2. Goldman R. "Curvature formulas for implicit curves and surfaces", Comput. Aided Geometric Design 22 (7), 632-658 (2005).

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Authors and Affiliations

  1. Moscow Pedagogical State University, 1 Malaya Pirogovskaya str., bdg. 1, 119991, Moscow, Russia

    A. M. Shelekhov

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  1. A. M. Shelekhov
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Correspondence to A. M. Shelekhov.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 11, pp. 54–66.

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Shelekhov, A.M. On the Curvatures of a Curve in n-Dimensional Euclidean Space. Russ Math. 65, 46–58 (2021). https://doi.org/10.3103/S1066369X21110062

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  • DOI: https://doi.org/10.3103/S1066369X21110062

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