Some New Characterizations of F-Rectifying Quaternionic Curves Respect to Type-2 Quaternionic Frame in Q4

Abstract

 Quaternions which are used in both theoritical and applied sciences, were defined by Hamilton in . Due to the wide application area for quaternions, there are numerous studies on the special defined quaternionic curves. In four dimensional spaces, rectifying curves are named as a curve whose position vector is completely lies in {T, N₂, N₃}. In this study, we present the notion of an f-rectifying quaternionic curve in Q⁴ as a quaternionic curve β in Q⁴ parametrized by its arc length s such that its f-position vector β_f= f(s)d_β for all s, every time lies in its rectifying space in Q⁴ where f is a nonzero integrable function in parameter s of the curve β. With the help of this information, we obtain some characterizations for such quaternionic curves in Q⁴.