Special Smarandache curves in R31

Abstract

In this work we continue to study negative AKNS(N ) that is AKNS(−N ) system for N = 3, 4. We obtain all possible local and nonlocal reductions of these equations. We construct the Hirota bilinear forms of these equations and find one-soliton solutions. From the reduction formulas we obtain also one-soliton solutions of all reduced equations. *

Smarandache Curves in three dimensional Lie groups

“…Proof. It is obvious using the equations ( 4) and (8).…”

“…Then, in [2], Smarandache curves were examined according to Darboux frame in Euclidean 3-space. Also, some researchers studied Smarandache curves in Minkowski space, [8,10]. Furthermore, in [9], Taşköprü and Tosun have investigated Smarandache curves according to Sabban Frame in Euclidean 3-space.…”

On Characterization of Smarandache Curves Constructed by Modified Orthogonal Frame

“…In this study, we investigated the Smarandache curves using the modified orthogonal frame to give a new perspective to curves. The Smarandache curves are characterized using different frames in Euclidean and non-Euclidean spaces [1][2][3][4][5][6][7][8][9]. The Smarandache curves obtained from spacelike Salkowski and anti-Salkowski curves are given by Eren and Şenyurt in Minkowski space [10][11][12][13].…”

3-Boyutlu Minkowski Uzayında İnvolüt-Evolüt Eğrilerinin T*B* ve N*B* -Smarandache Eğrileri

“…Gürses. vd., 3 1 R de spacelike, timelike ve null eğrilerin TN -Smarandache eğrilerini incelemişlerdir [6]. Şenyurt ve Sivas, Öklid uzayında bir eğrinin asli normali ve Darboux vektörünü konum vektörü alarak elde edilen Smarandache eğrilerinin eğriliklerini hesaplamışlardır [9].…”