Smarandache curves in Euclidean 4- space E 4

Some special Smarandache curves according to the extended Darboux frame in $mathbb{E}^4_1$

“…The Minkowski 4-space E 4 1 is the real vector space R 4 provided with the indefinite flat metric given by…”

“…In this study, considering the extended Darboux frame (or shortly ED-frame) in Minkowski 4-space [8], we define some special Smarandache curves according to the ED-frame in E 4 1 . Then we obtain the Frenet apparatus of TD-Smarandache curve depending on the invariants of the ED-frame of second kind.…”

Smarandache Curves According to the Extended Darboux Frame in Euclidean 4-Space

“…A regular curve, whose position vector is obtained by Frenet frame vectors on another regular curve is called Smarandache curve in Minkowski space-time [1]. Special Smarandache curves have been studied at many researches in both Euclidean space and Minkowski space [1][2][3][4][5]. There are also some studies on special Smarandache curves in Galilean and pseudo-Galilean spaces [6][7][8].…”

“…In this study, the authors have calculated the Frenet apparatus of these special Smarandache curves and found some properties of these curves. Also, Smarandache curves in 4-dimensional Euclidean space according to the Frenet frame and parallel transport frame have been studied in [5] and obtained the Frenet-Serret and Bishop invariants for the Smarandache curves.…”

Some special curves belonging to Mannheim curves pair

“…A regular curve in Minkowski spacetime whose position vector is composed by Frenet frame vectors is called a Smarandache curve [4]. Special Smarandache curves have been studied by some authors [5][6][7][8][9][10]. Taskopru and Tosun [11] studied special Smarandache curves according to Sabban frame on 2 S .…”