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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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A characterization of ccr-curves in Rm; pp. 217–224

(Full article in PDF format) doi: 10.3176/proc.2008.4.03


Authors

Günay Öztürk, Kadri Arslan, H. Hilmi Hacisalihoglu

Abstract

We study the curve in Rm  for which the ratios between two consecutive curvatures are constant (ccr-curves). We show that closed ccr-curves in Euclidean space Rm  are of finite type. We also consider Frenet curves with constant harmonic curvatures and show that an immersed curve in R2n+1   with constant harmonic curvatures Hi at point γ (s0)   has a Darboux vertex at that point.

Keywords

differential geometry, Frenet curve, W-curve, curves of finite type, ccr-curve.

References

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Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December