Khadzhiev, D. and Oren, I. (2019) Global Invariants of Paths and Curves for the Group of Orthogonal Transformations in the Two-Dimensional Euclidean Space. Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica, 27, 37-65.
https://doi.org/10.2478/auom-2019-0018

has been cited by the following article:

• TITLE: Equivalence of Paths under the Action of the Real Representation of Sp(n)

  AUTHORS: Muminov K. Khodyrovich, Juraboyev S. Solyjonovich

  KEYWORDS: Real Representation, Differential Invariant, Differential Generators, Path in a Finite-Dimensional Space

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.5, May 31, 2022

  ABSTRACT: In this article, we will consider questions of G-equivalence of paths for the case when G was the group of the real representation of a symplectic transformation in an n-dimensional quaternion vector space. In determining the solution of this problem, we give an explicit description of differential generators of a differential field of differential rational functions that are invariant under the action of this group. Necessary and sufficient conditions for the G-equivalence of paths in a 4n-dimensional real space are obtained with the help of differential generators.