2020 # Ruled Surfaces and Tangent Bundle of Unit 2-Sphere of Natural Lift Curves

**Abstract:** Highlights• A unique ruled surface is corresponded to the natural lift curve.• Properties of ruled surfaces generated by natural lift curves are examined. • A method is given for modelling motions on ̅ instead of 2 .

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“…is the ruled surface in 3 corresponding to the dual curve 2 Γ(s) = q(s) + εv(s) DS (or to the natural lift curve Γ(s) TM ) in [19]. Considering the ruled surface given in Eq.…”

confidence: 99%

“…is the ruled surface in 3 corresponding to the dual curve 2 Γ(s) = q(s) + εv(s) DS (or to the natural lift curve Γ(s) TM ) in [19]. Considering the ruled surface given in Eq.…”

confidence: 99%

“…In the light of this study, a one-to-one correspondence between and is mentioned in [18]. In that study, according to E. Study mapping, to each curve on corresponds a ruled surface in Euclidean 3-space, Furthermore, exploiting this relation, each curve on corresponds a ruled surface in Then, inspired by [18], the isomorphism among , the subset of the tangent bundle of unit 2-sphere, and the ruled surface generated by natural lift curves in are examined in [19]. Furthermore, the developability condition of this ruled surface is given in the same study.…”

confidence: 99%

“…A ruled surface is defined by a straight line that is moving along a curve [1]. Many mathematicians have studied the ruled surfaces [2][3][4][5][6][7][8]. E. Ergün and M. C ¸alışkan [2] created ruled surfaces by accepting the natural lift of a curve as the base curve and they characterized these surfaces.…”

confidence: 99%

“…The natural lift curve is defined as the curve drawn by the endpoints of the unit tangent vector at each point of a given curve. Many mathematicians have studied on natural lift curves [2][3][4][5][6]. The Frenet vectors of the natural lift curve were introduced by C ¸alıs ¸kan and Ergün with regard to the Frenet vectors of the main curve [5].…”

confidence: 99%