Research ArticleNo Access

Motions of Curves in 4-Dimensional Galilean Space $G_{4}$

Hülya Gün Bozok

Department of Mathematics, Faculty of Arts and Sciences, Osmaniye Korkut Ata University, Osmaniye, Turkey

E-mail Address: hulyagun@osmaniye.edu.tr

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Sezin Aykurt Sepet

Department of Mathematics, Faculty of Arts and Sciences, Kırşehir Ahi Evran University, Kırşehir, Turkey

E-mail Address: sezinaykurt@hotmail.com

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Mahmut Ergüt

Department of Mathematics, Faculty of Arts and Sciences, Tekirdağ Namik Kemal University, Tekirdağ, Turkey

E-mail Address: mergut@nku.edu.tr

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https://doi.org/10.1142/S1793557121501539Cited by:0 (Source: Crossref)

Abstract

In this paper, we investigate the flow of curve and its equiform geometry in 4-dimensional Galilean space. We obtain that the Frenet equations and curvatures of inextensible flows of curves and its equiformly invariant vector fields and intrinsic quantities are independent of time. We find that the motions of curves and its equiform geometry can be defined by the inviscid and stochastic Burgers’ equations in 4-dimensional Galilean space.

Communicated by I. Inam

Keywords:

AMSC: 53A35, 53C44

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