2016FilomatOpen access

Constant curvature ratios in L6

Esen İyigün

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Abstract

In this paper, we find a relation between Frenet formulas and harmonic curvatures, and also a relation between Frenet formulas and e-curvature functions of a curve of osculating order 6 in 6 dimensional Lorentzian space L6. Moreover, we give a relation between harmonic curvatures and ccr-curves of a curve in L6.

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What this paper is about

In this paper, we find a relation between Frenet formulas and harmonic curvatures, and also a relation between Frenet formulas and e-curvature functions of a curve of osculating order 6 in 6 dimensional Lorentzian space L6. Moreover, we give a relation between harmonic curvatures and ccr-curves of a curve in L6.

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Available abstract

In this paper, we find a relation between Frenet formulas and harmonic curvatures, and also a relation between Frenet formulas and e-curvature functions of a curve of osculating order 6 in 6 dimensional Lorentzian space L6. Moreover, we give a relation between harmonic curvatures and ccr-curves of a curve in L6.

Key concepts: Frenet–Serret formulas, Osculating circle, Mathematics, Curvature, Torsion of a curve, Mathematical analysis, Constant (computer programming), Harmonic

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