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On Standard Paths with Constant Inner Curvatures on a Sphere in a Pseudo-Euclidean Space


We prove that every standard path with constant inner curvatures on a sphere in a pseudo-Euclidean space \({\mathbb {E}}^n_l\), \(n\ge 3 \), of an arbitrary index \(l \) is an orbit of a one-parameter subgroup of the group of motions of the sphere.

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The work was supported by the Program of Fundamental Scientific Research of the SB RAS No. I.1.1., project No. 0314-2019-0004.

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Correspondence to I. A. Zubareva.

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Zubareva, I.A. On Standard Paths with Constant Inner Curvatures on a Sphere in a Pseudo-Euclidean Space. Sib. Adv. Math. 31, 69–77 (2021).

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  • standard path
  • inner curvature
  • Frenet frame
  • orbit of a one-parameter group of isometries
  • pseudo-Euclidean space