New Characterizations for Spherical Indicatrices of Involutes of a Spacelike Curve With a Timelike Binormal in Minkowski 3-Space

Abstract

In this paper, we study the spherical indicatrices of involutes of a spacelike curve with spacelike binormal. Then we give some important relationships between arc lengths and geodesic curvatures of the spherical indicatrices of involute-evolute curve couple in Minkowski 3-space. Also, we give some important results about curve couple.

A Survey on Timelike-Spacelike Involute-Evolute Curve Pair

“…Moreover, there are also many studies on spherical indicatrix curves and the n.l.c in Euclidean space and Lorentz space [9][10][11][12][13][14][15]. Recently, authors have found the relations between the Frenet vectors of the curve pair in the Lorentz 3-space [16]. These relationships were the source of inspiration for this study.…”

“…We know from [7] that "The n.l.c  of the curve  is an integral curve of the geodesic spray W if and only if  is a geodesic on M ".…”

“…,  be the involute-evolute curve pair. The following equality [16] gives the Frenet vectors of the curve pair:…”

“…In [6], Bilici et al generalized this problem to spherical indicatrices of the involute-evolute curve pair. Later, the authors adapted this problem for a non-null curves in the three dimensional Lorentz spaces [7,8]. Moreover, there are also many studies on spherical indicatrix curves and the n.l.c in Euclidean space and Lorentz space [9][10][11][12][13][14][15].…”

“…Later, the authors adapted this problem for a non-null curves in the three dimensional Lorentz spaces [7,8]. Moreover, there are also many studies on spherical indicatrix curves and the n.l.c in Euclidean space and Lorentz space [9][10][11][12][13][14][15]. Recently, authors have found the relations between the Frenet vectors of the curve pair in the Lorentz 3-space [16].…”