Geodesic
On the curvatures of a curve in $n$-dimensional Euclidean space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2021), pp. 54-66

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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. 
@article{IVM_2021_11_a5,
     author = {A.M. Shelekhov},
     title = {On the curvatures of a curve in $n$-dimensional {Euclidean} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {54--66},
     publisher = {mathdoc},
     number = {11},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_11_a5/}
}
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A.M. Shelekhov. On the curvatures of a curve in $n$-dimensional Euclidean space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2021), pp. 54-66. http://geodesic.mathdoc.fr/item/IVM_2021_11_a5/