On invariants of null curves in the pseudo-Euclidean geometry

Pekşen, Ömer; Khadjiev, Djavvat

doi:10.1016/j.difgeo.2011.04.024

Cited by 7 publications

(5 citation statements)

References 13 publications

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“…Below J ⊆ R, where J is a one of sets (0, l), l < +∞; (0, +∞), (−∞, 0) or (−∞, +∞). This equality, equalities (16) and (17) imply that x(s) has the form (21) Conversely, assume that x(s) has the form (21) or the form (22). Then, by ∼ β.…”

Section: The Type and Invariant Parametrizations Of An L-nondegeneratmentioning

confidence: 99%

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Global invariants of paths and curves for the group of orthogonal transformations in the two-dimensional Euclidean space

Khadjiev

Ören

2019

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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In this paper, for the orthogonal group G = O(2) and special orthogonal group G = O+(2) global G-invariants of plane paths and plane curves in two-dimensional Euclidean space E2 are studied. Using complex numbers, a method to detect G-equivalences of plane paths in terms of the global G-invariants of a plane path is presented. General evident form of a plane path with the given G-invariants are obtained. For given two plane paths x(t) and y(t) with the common G-invariants, evident forms of all transformations g ∈ G, carrying x(t) to y(t), are obtained. Similar results have obtained for plane curves.

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Section: The Type and Invariant Parametrizations Of An L-nondegeneratmentioning

confidence: 99%

“…Moreover, systems of generators of differential field of G-invariant differential rational functions of a path in E n for groups M (n) and M + (n) are obtained . This approach was developed for curves in papers [15,16,21,22] and for vector fields in [13,14].…”

Section: Introductionmentioning

confidence: 99%

Global invariants of paths and curves for the group of orthogonal transformations in the two-dimensional Euclidean space

Khadjiev

Ören

2019

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…Complete systems of global G-invariants of regular paths and regular curves in classical geometries were obtained in [2,7]. This approach was developed for curves in papers [10,11,17,18] and for vector fields in [8,9].…”

Section: Introductionmentioning

confidence: 99%

Recognition of Paths and Curves in the 2-Dimensional Euclidean Geometry

Ören

Khadjiev

2020

International Electronic Journal of Geometry

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This paper presents global differential invariants of curves and paths in the 2-dimensional Euclidean geometry for the groups of Euclidean transformations M (2) and special Euclidean transformations M + (2). For these groups, analogues of the fundamental theorem for Euclidean curves are obtained in terms of global differential invariants of a path and a curve. Moreover, for given two paths(or curves) with the common differential G-invariants, evident forms of all Euclidean transformations that maps one of the paths (or curves) to the other are found.

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“…The invariants of vectors and curves relative to the Euclidean group, a¢ ne group and Lorentz group are investigated in [1,2,5,6,7,8]. Some applications of the invariant theory are given in [3,4].…”

Section: Introductionmentioning

confidence: 99%