On The Modified Orthogonal Frame with Curvature and Torsion in 3-Space

Abstract

In this paper, we study the modified orthogonal vector fields with curvature and torsion of a space curve in Minkowski 3-Space.

Some Characterizations of Tubular Surfaces and their Focal Surfaces in Euclidean 3-Space

“…Therefore, the frame denoted by Eq. (2.5) is called the modified orthogonal frame with curvature [11].…”

“…Sasai [10] described the modified orthogonal frame of a space curve in Euclidean 3-space as a helpful tool for examining analytic curves with singular points when the Frenet frame is ineffective. The modified orthogonal frame has recently been the subject of various investigations [11][12][13][14][15][16].…”

Modified Roller Coaster Surface in Space

“…where g(, ) denotes the inner product of E 3 . We note that the essential quantities in Equations 6and 7are κ 2 and τ(s) which are analytic in s [26][27][28].…”

On tubular surfaces with modified orthogonal frame in Galilean space G3

“…For example, tubular surfaces in Minkowski space [12,13] and tubular surfaces in Galilean space were investigated in studies [14][15][16]. Then, a lot of papers were studied on "Modified Orthogonal Frame" [17][18][19][20][21][22][23][24][25].…”