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2012•Bursa Uludag University - AVESISRequires access

Curves with constant curvature ratios in L5

Esen İyigün

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Abstract

In this study, we first give a relation between  Frenet formulas and harmonic curvatures of a curve of osculating order 5 in L⁵. Also, we find a relation between harmonic curvatures and ccr -curves of a curve in L⁵ and also obtain some results. Finally, we calculate constant curvature ratios e₁((k₂)/(k₁)), e₂((k₃)/(k₂)), e₃((k₄)/(k₃)) of the unit speed time-like curve in L⁵ studied in [3].

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What this paper is about

In this study, we first give a relation between  Frenet formulas and harmonic curvatures of a curve of osculating order 5 in L⁵. Also, we find a relation between harmonic curvatures and ccr -curves of a curve in L⁵ and also obtain some results. Finally, we calculate constant curvature ratios e₁((k₂)/(k₁)), e₂((k₃)/(k₂)), e₃((k₄)/(k₃)) of the unit speed time-like curve in L⁵ studied in [3].

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Available abstract

In this study, we first give a relation between  Frenet formulas and harmonic curvatures of a curve of osculating order 5 in L⁵. Also, we find a relation between harmonic curvatures and ccr -curves of a curve in L⁵ and also obtain some results. Finally, we calculate constant curvature ratios e₁((k₂)/(k₁)), e₂((k₃)/(k₂)), e₃((k₄)/(k₃)) of the unit speed time-like curve in L⁵ studied in [3].

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

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