Camci, CetinChen, Bang-YenIlarslan, KazimUcum, Ali2025-01-212025-01-2120210047-24681420-8997https://doi.org/10.1007/s00022-021-00610-6https://hdl.handle.net/20.500.12587/25438Associated with a Frenet curve alpha in Euclidean 3-space E-3, there exists the notion of natural mate beta of alpha. In this article, we extend the natural mate beta to sequential natural mates {alpha(1), alpha(2), . . . , alpha(n alpha)} with alpha(1) = beta. We call each curve alpha(i), i epsilon {1, 2, . . . , n(alpha)}, the i-th natural mate. The main purpose of this article is to study the relationships between the given Frenet curve a with its sequential natural mates {alpha(1), alpha(2), . . . , alpha n(alpha)}.eninfo:eu-repo/semantics/closedAccessAnti-Salkowski curve; Bertrand curve; general helices; ith natural mate; Mannheim curve; natural mates; Salkowski curve; sequential natural mateArticle112310.1007/s00022-021-00610-62-s2.0-85118249868Q3WOS:000711414600001N/A