Smarandache Curves of Natural Curves Pair According to Frenet Frame
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.
*Author to whom correspondence should be addressed.
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.
Keywords: Smarandache curves, natural mate curves, Frenet apparatus