Equiform spacelike normal curves according to equiform‐Bishop frame in

Abstract

In this article, we present the equiform parameter and define the equiform-Bishop frame in Minkowski 3-space E 3 1 . Additionally, we investigate the equiform-Bishop formulas of the equiform spacelike case in Minkowski 3-space.Furthermore, some results of equiform spacelike normal curves according to the equiform-Bishop frame in E 3 1 are considered. KEYWORDS equiform-Bishop frame, equiform curvatures, Minkowski Space, normal curves PRELIMINARIESThe Minkowski space E 3 1 is the space R 3 , equipped with the metric g, where g is given bywhere (x 1 , x 2 , x 3 ) is a coordinate system of E 3 1 . Let v be any vector in E 3 1 , then the vector v is spacelike, timelike, or null (lightlike) if g(v, v) > 0 or v = 0, g(v, v) < 0 or g(v, v) = 0, and v ≠ 0. The causal character of a vector in Minkowski space is the property to be spacelike, timelike, or null (lightlike).

Characterizations of Tzitzeica curves using Bishop frames

“…So there is an alternative way to define the moving reference frame that was introduced by Bishop 11 in 1975 by means of parallel vector fields and the so‐called as alternative or parallel‐adapted frame of the curves. Recently, some researchers called this frame as Bishop frame, and this frame‐based studies have been intensively treated, see other studies 12–19 . In this study, the conditions of a regular curve to be a Tzitzeica curve according to Bishop Type‐1 and Type‐2 frames in Euclidean 3‐space have been investigated.…”

“…Recently, some researchers called this frame as Bishop frame, and this frame-based studies have been intensively treated, see other studies. [12][13][14][15][16][17][18][19] In this study, the conditions of a regular curve to be a Tzitzeica curve according to Bishop Type-1 and Type-2 frames in Euclidean 3-space have been investigated.…”

Quaternionic Bertrand curves in the Galilean space

“…The geometry of curves in both Euclidean and Minkowski spaces was represented for many years a popular topic in the field of classical differential geometry [4][5][6]11]. Global and local properties were studied in several books and new invariants were defined for curves.…”