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Research Article Open access CC BY 4.0

Smarandache Curves of Natural Curves Pair According to Frenet Frame

Thiago Mendonca, Jose Alan, Renato Teixeira

Advances in Research · pp. 1–13 · Published 23 Aug 2024

10.9734/air/2024/v25i51131

Abstract

Smarandache curves play a significant role in differential geometry. They extend conventional differential geometry concepts and help uncover novel geometric properties. In this work, we define the Smarandache curves of the Natural mate of any given curve \(\alpha\) and calculate their Frenet apparatus. As a particular case, we present the Frenet apparatus when \(\alpha\) is a helix. Additionally, we illustrate an example for the slant helix.

Smarandache curves natural mate curves Frenet apparatus

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Cited by 6

Adjoint curves of special Smarandache curves with respect to Bishop frame

Esra Damar · AIMS Mathematics · 2024

A Novel Approach to Ruled Surfaces Using Adjoint Curve

Esra Damar · Symmetry · 2025

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