Spacelike and timelike admissible Smarandache curves in pseudo-Galilean space

Abstract

In this paper, space and timelike admissible Smarandache curves in the pseudo-Galilean space G 1 3 are investigated. Also, Smarandache curves of the position vector of space and timelike arbitrary curve and some of its special curves in G 1 3 are obtained. To confirm our main results, some examples are given and illustrated. M.S.C. 2010 : 53A35, 53B30.

Computing Special Smarandache Curves According to Darboux Frame in Euclidean 4-Space

“…Let {T, P, U, N} be a Darboux frame field of first kind along r(u) and κ n , κ 1 g , κ 2 g , τ 1 g , τ 2 g are real valued functions in arc length parameter u of r. So, we have the following definition. In the following we continue our studies of special Smarandache curves that we started in [2,5,6]. Here we investigate some special Smarandache curves of first kind called TP, TU, PU and PN ( the other special Smarandache curves can be computed in the same manner) and then obtain some of their differential geometric properties which represent the main results.…”

“…Smarandache curves are the objects of Smarandache geometry. By definition, if the position vector of a curve δ is composed by Frenet frame's vectors of another curve β, then the curve δ is called a Smarandache curve [2].…”

“…In the light of the existing studies in the field of geometry, many interesting results on Smarandache curves have been obtained by many mathematicians, see for example, [2,3,[5][6][7][8][9][10][11][12]. Turgut and Yilmaz [11] have introduced a particular circumstance of such curves, they entitled it Smarandache TB 2 curves in the space E 1 4 .…”

“…Recently, H.S. Abdel-Aziz and M. Khalifa Saad [2,5] have studied special Smarandache curves of an arbitrary curve such as TN, TB and TNB with respect to Frenet frame in the three-dimensional Galilean and pseudo-Galilean spaces. Also, in [6,7] they have investigated Smarandache curves according to Darboux frame in the three-dimensional Minkowski space E 3 1 .…”

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

“…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].…”