Some New Characterizations of F-Rectifying Curves Respect to Type-2 Quaternionic Frame in R^4

Abstract

Quaternions which are used in both theoriticial and applied sciences, were defined by Hamilton in 1843. 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 curve in ℝ4 as a curve 𝛽 in ℝ4 parametrized by its arc length s such that its f-position vector 𝛽𝑓 (𝑠) = 𝑓(𝑠)𝑑𝛽 for all s, every time lies in its rectifying space in ℝ4 , 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 curves ın ℝ4.