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2000•Communications Faculty Of Science University of Ankara Series A1Mathematics and StatisticsOpen access

On harmonic curvatures of a frenet curve

Hilmi H. HACISALİHOĞLU, Kadri Arslan

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Abstract

In this paper we craısider hannonic curvatures of a Frenet curve of osculating order d. We also consider a general helix of AW(k) type where k=l,2 and 3. We have show that, there is no general helix of AW(3)type. We also show that, a general helix of rank 1 and of AW(3) type must be a circular helix. We give curvature conditions of the curves, whid) have AW(2) prt^aty. In the final part, we visualize the plane and space curves of (weak) AW(2) type.

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What this paper is about

In this paper we craısider hannonic curvatures of a Frenet curve of osculating order d. We also consider a general helix of AW(k) type where k=l,2 and 3. We have show that, there is no general helix of AW(3)type. We also show that, a general helix of rank 1 and of AW(3) type must be a circular helix. We give curvature conditions of the curves, whid) have AW(2) prt^aty. In the final part, we visualize the plane and space curves of (weak) AW(2) type.

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Available abstract

In this paper we craısider hannonic curvatures of a Frenet curve of osculating order d. We also consider a general helix of AW(k) type where k=l,2 and 3. We have show that, there is no general helix of AW(3)type. We also show that, a general helix of rank 1 and of AW(3) type must be a circular helix. We give curvature conditions of the curves, whid) have AW(2) prt^aty. In the final part, we visualize the plane and space curves of (weak) AW(2) type.

Key concepts: Frenet–Serret formulas, Osculating circle, Helix (gastropod), Curvature, Plane curve, Mathematics, Torsion of a curve, Type (biology)

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