Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2024; 61(3): 849-866

Online first article May 23, 2024      Printed May 31, 2024

https://doi.org/10.4134/BKMS.b230491

Copyright © The Korean Mathematical Society.

A non-Newtonian approach in differential geometry of curves: multiplicative rectifying curves

Muhittin Evren Aydın , Aykut Has , Beyhan Yılmaz

Firat University; Kahramanmaras Sutcu Imam University; Kahramanmaras Sutcu Imam University

Abstract

In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension $3$, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not metric, we are directly able to perform multiplicative differential-geometric concepts to investigate such curves. By several characterizations, we completely classify the multiplicative rectifying curves by means of the multiplicative spherical curves.

Keywords: Rectifying curve, spherical curve, multiplicative calculus, multiplicative Euclidean space

MSC numbers: Primary 53A04; Secondary 11U10, 08A05

Supported by: This study was supported by Scientific and Technological Research Council of Turkey (TUBITAK) under the Grant Number 123F055. The authors thank to TUBITAK for their supports..