Spherical Indicatrix Curves in Multiplicative Euclidean Space

Year 2025, Volume: 2 Issue: 2, 83 - 99, 27.11.2025

İlkay Arslan Güven , Murat Korkmaz

Abstract

The goal of this study is to investigate spherical indicatrix curves in multiplicative space R_*. Spherical indicatrix curves that develop on the surface of sphere, are one of the type of associated curves. By considering the multiplicative Frenet frame of a multiplicative curve in three dimensional multiplicative Euclidean space, there are three multiplicative indicatrix curves: tangent indicatrix, principal normal indicatrix and binormal indicatrix curves. We obtain the Frenet apparatus of these curves in terms of multiplicative derivative and calculations and give some characterizations about being multiplicative Bertrand and involute-evolute curve pairs between the indicatrix curves. We also demonstrate relations between the main multiplicative curve and indicatrix curves. Lastly, we exemplify with the figures which supports the theory in this study.

Keywords

Multiplicative space , Multiplicative calculus , Indicatrix curves , Multiplicative sphere

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