A characterization of ccr-curves in R-m

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

PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES, cilt.57, sa.4, ss.217-224, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 57 Sayı: 4
  • Basım Tarihi: 2008
  • Doi Numarası: 10.3176/proc.2008.4.03
  • Dergi Adı: PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.217-224
  • Anahtar Kelimeler: differential geometry, Frenet curve, W-curve, curves of finite type, ccr-curve
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.