Construction of vectorial moments via direction curves

Semra Kaya Nurkan; İlkay Arslan Güven; Semra Kaya Nurkan; İlkay Arslan Güven

doi:10.3934/math.2023648

AIMS Mathematics

2023, Volume 8, Issue 6: 12857-12871. doi: 10.3934/math.2023648

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Construction of vectorial moments via direction curves

Semra Kaya Nurkan ^{1
,
,},
İlkay Arslan Güven ²

1.
Department of Mathematics, Faculty of Arts and Science, Usak University, TR-64200 Uşak, Turkey
2.
Department of Mathematics, Faculty of Arts and Science, Gaziantep University, TR-27310 Gaziantep, Turkey

Received: 23 December 2022 Revised: 15 March 2023 Accepted: 20 March 2023 Published: 31 March 2023
MSC : 53A04, 53Z05

In a recent paper Tunçer ^[14] described and examined the moment vectors (T -dual, N-dual, B-dual curve) of the curve with respect to the origin of the vector by using T(s), N(s), B(s) and the position vector of the curve. With the inspiration this paper provided, we define some new associated curves called dual-direction curves as integral curves of a vector field in this study. They are generated with the help of vectorial moments of a space curve in three-dimensional Euclidean space. We attain some connections between the Frenet apparatus of dual-direction curves and main curves. With the help of these dual-direction curves, certain ways to construct helices are determined. Finally, we exemplify these curves with their figures.
- associated curves,
- direction curves,
- integral curves,
- vectorial moment,
- general helices
Citation: Semra Kaya Nurkan, İlkay Arslan Güven. Construction of vectorial moments via direction curves[J]. AIMS Mathematics, 2023, 8(6): 12857-12871. doi: 10.3934/math.2023648

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Abstract

In a recent paper Tunçer ^[14] described and examined the moment vectors (T -dual, N-dual, B-dual curve) of the curve with respect to the origin of the vector by using T(s), N(s), B(s) and the position vector of the curve. With the inspiration this paper provided, we define some new associated curves called dual-direction curves as integral curves of a vector field in this study. They are generated with the help of vectorial moments of a space curve in three-dimensional Euclidean space. We attain some connections between the Frenet apparatus of dual-direction curves and main curves. With the help of these dual-direction curves, certain ways to construct helices are determined. Finally, we exemplify these curves with their figures.

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