Sequential natural mates of Frenet curves in Euclidean 3-space

Associated with a Frenet curve α in Euclidean 3-space E 3 , there exists the notion of natural mate β of α . In this article, we extend the natural mate β to sequential natural mates { α 1 , α 2 , … , α n α } with α 1 = β . We call each curve α i , i ∈ { 1 , 2 , … , n α } , 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 { α 1 , α 2 , … , α n α } .