Vectorial moments of curves in Euclidean 3-space

Abstract

In this study, we introduced the vectorial moments as a new curves as [Formula: see text]-dual curve, where [Formula: see text], constructed by the Frenet vectors of a regular curve in Euclidean 3-space and we gave the Frenet apparatus of [Formula: see text]-dual curves and also we applied to helices and curve pairs of constant breadth.

Curves and ruled surfaces according to alternative frame in dual space

“…where principal normal vector N is same in both frames, = and = , [11,19]. [18]. By di¤erentiating both side of (10), it is obtained [18]…”

“…Let f (s), g(s) and h(s) be al least C 3 functions. (s) can be written in the form of (s) = f (s)T (s) + g(s)N (s) + h(s)B(s) (10) as a linear combination of the Frenet vectors fT; N; Bg, [18]. By di¤erentiating both side of (10), it is obtained [18]…”

A Different View on Dynamics of Space Curves Geometry

“…If a curve is a linear combination of constant multiples of Frenet vectors of another curve, the curve is called a Smarandache curve [11]. Tuncer, defined and examined the moment vectors ( T− dual, N−dual and B−dual curve) of the curve with respect to the origin of the vector by using T(s) , N(s) , B(s) vector and by using the position vector of the curve [5]. Şenyurt et al examined the vectorial moment of the unit Darboux vector [12].…”

“…Şenyurt and Çalışkan expressed and examined the vectorial moments in terms of alternative frame and they applied these to ruled surfaces [13]. If T−dual, N−dual and B−dual curves of a curve are denoted by L T (s) , L N (s) and L B (s) according to the origin, then these curves are defined as respectively [5].…”