The integrability for the derivative formulas of the type-2 2 Bishop frame and its applications

Abstract

The main objective of the work is to examine the integrability of the derivative formulae for the type-2 Bishop frame in three-dimensional Euclidean space. We use the coordinate system introduced in \cite{yer1}, which allows for the examination of integration. As an application, we analyze the position vectors of certain curves that are important in mathematics and physical study.