A non-Newtonian some partner curves in multiplicative Euclidean space

TL;DR

This paper explores the properties and characterizations of classical partner curves like Bertrand and Mannheim curves within multiplicative Euclidean spaces, extending differential geometry concepts to non-Newtonian multiplicative analysis.

Contribution

It introduces multiplicative versions of Bertrand and Mannheim partner curves and characterizes their properties using multiplicative Frenet vectors and analysis.

Findings

Defined multiplicative Bertrand and Mannheim curves

Characterized these curves using multiplicative Frenet vectors

Provided examples and multiplicative graphs for illustration

Abstract

The aim of this article is to characterize pairs of curves within multiplicative (non-Newtonian) spaces. Specifically, we investigate how famous curve pairs such as Bertrand partner curves, Mannheim partner curves, which are prominent in differential geometry, are transformed under the influence of multiplicative analysis. By leveraging the relationships between multiplicative Frenet vectors, we introduce multiplicative versions of Bertrand, Mannheim curve pairs. Subsequently, we characterize these curve pairs using multiplicative arguments. Examples are provided, and multiplicative graphs are presented to enhance understanding of the subject matter. Through this analysis, we aim to elucidate the behavior and properties of these curve pairs within the context of multiplicative geometry.