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2014•arXiv (Cornell University)Open access

Generalized Similar Frenet Curves

Fatma Gökçelik, Seher Kaya, Yusuf Yaylı, F. Nejat Ekmekci

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Abstract

The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then, these invariants expressed by focal curvatures of the curve. And then, we give the relationship between curvatures of evolute curve and shape curvatures. Morever, these invariants is given the geometric interpretation.

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What this paper is about

The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then, these invariants expressed by focal curvatures of the curve. And then, we give the relationship between curvatures of evolute curve and shape curvatures. Morever, these invariants is given the geometric interpretation.

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Available abstract

The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then, these invariants expressed by focal curvatures of the curve. And then, we give the relationship between curvatures of evolute curve and shape curvatures. Morever, these invariants is given the geometric interpretation.

Key concepts: Frenet–Serret formulas, Arc length, Similarity (geometry), Interpretation (philosophy), Mathematics, Euclidean geometry, Torsion of a curve, Mathematical analysis

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