A characterization of ccr-curves in R-m

Ozturk G., ARSLAN K., HACISALİHOĞLU H. H.

PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES, vol.57, no.4, pp.217-224, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 4
  • Publication Date: 2008
  • Doi Number: 10.3176/proc.2008.4.03
  • Journal Name: PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.217-224
  • Keywords: differential geometry, Frenet curve, W-curve, curves of finite type, ccr-curve
  • Bursa Uludag University Affiliated: Yes

Abstract

We study the curve in R-m for which the ratios between two consecutive curvatures are constant (ccr-curves). We show that closed ccr-curves in Euclidean space R-m 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 H-t at point gamma(s(0)) has a Darboux vertex at that point.