On osculating, normal and rectifying bi-null curves in ℝ⁶₃

Normal curves in n-dimensional Euclidean space

“…If Eqs. (12) and (13) are written in 7, then the statement (17) is obtained. Conversely, suppose that there is a relationship between curvatures as in (17).…”

“…Substituting (8)- (13) into (18), and taking the inner product of the both sides of (18) with α(s) -Y (s), then we get the following relations:…”

“…Normal and rectifying curves are defined in Galilean space in [11] and [12]. The osculating, normal and rectifying binull curves in R 6 3 and R 5 2 are given in [13] and [14]. The concept of a normal curve is given by quaternions in Euclidean space; the semi Euclidean space was addressed by Yıldız and Karakus in [15] and [16].…”

Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space

“…Normal, osculating and rectifying curves have been defined in the Euclidean and semi Euclidean space by using quaternion algebra in [10], [11], [16] and [25]. Bi-null curves of these types have also been analyzed in R 6 3 and R 5 2 in [12,13]. Several studies in the literature on the topic of interest of this study can be found in [14-18, 26, 27].…”