Sequential natural mates of Frenet curves in Euclidean 3-space

Abstract

Associated with a Frenet curve α in Euclidean 3-space E3, there exists the notion of natural mate β of α. In this article, we extend the natural mate β to sequential natural mates {α1,α2,…,αnα} with α1= β. We call each curve αi, i∈ { 1 , 2 , … , nα} , the i-th natural mate. The main purpose of this article is to study the relationships between the given Frenet curve α with its sequential natural mates {α1,α2,…,αnα}.