Skip to main content

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

Abstract

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.

This is a preview of subscription content, access via your institution.

REFERENCES

  1. 1

    Yu. A. Aminov, Differential Geometry and Topology of Curves (Nauka, Moscow, 1987) [Differential Geometry and Topology of Curves (Gordon and Breach Science Publishers, Amsterdam, 2000)].

  2. 2

    Yu. F. Borisov, “Removing the a priori restrictions in the theorem on a complete system of invariants of a curve in \({\mathbb E}^n_l\),” Sib. Matem. Zh. 38, 485 (1997) [Siberian Math. J. 38, 411 (1997)].

    MathSciNet  Article  Google Scholar 

  3. 3

    S. V. Sizyĭ, Lectures in Differential Geometry (Fizmatlit, Moscow, 2007) [in Russian].

    MATH  Google Scholar 

  4. 4

    R. Sulanke, The Fundamental Theorem for Curves in the \(n\)-Dimensional Euclidean Space (Manuscript available at http://www-irm.mathematik.hu-berlin.de/ sulanke/diffgeo/euklid/ECTh.pdf).

  5. 5

    I. A. Zubareva, “On curves with constant curvatures in a pseudo-Euclidean space,” Matem. Struktury Model. no. 4, 21 (2018) [in Russian].

Download references

Funding

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

Author information

Affiliations

Authors

Corresponding author

Correspondence to I. A. Zubareva.

About this article

Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1134/S1055134421010077

Download citation

Keywords

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