Smarandache Curves of Natural Curves Pair According to Frenet Frame

Thiago Mendonca; Jose Alan; Renato Teixeira

doi:10.9734/air/2024/v25i51131

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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Thiago Mendonca, Jose Alan, Renato Teixeira (2024). Smarandache Curves of Natural Curves Pair According to Frenet Frame. Advances in Research , 1–13. https://doi.org/10.9734/air/2024/v25i51131

Affiliations

Thiago Mendonca — Departamento de Matematica, UFRPE, Rua Manoel de Medeiros, s/n - Dois Irmaos, Recife - PE, 52171-900, Brazil.
Jose Alan — Departamento de Matematica, UFRPE, Rua Manoel de Medeiros, s/n - Dois Irmaos, Recife - PE, 52171-900, Brazil.
Renato Teixeira — Departamento de Matematica, UFRPE, Rua Manoel de Medeiros, s/n - Dois Irmaos, Recife - PE, 52171-900, Brazil.

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