On the explicit characterization of curves on a n 1 sphere in S n
Yazarlar (4)
C. Camci
Prof. Dr. Levent KULA Kırşehir Ahi Evran Üniversitesi, Türkiye
K. Ilarslan
H. H. Hacisalihoglu
| Makale Türü |
Özgün Makale
(Uluslararası alan indekslerindeki dergilerde yayınlanan tam makale)
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| Dergi Adı | INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY | ||
| Dergi ISSN | 1307-5624 | ||
| Dergi Tarandığı Indeksler | MathSciNet | ||
| Makale Dili | İngilizce | Basım Tarihi | 10-2013 |
| Cilt / Sayı / Sayfa | 6 / 2 / 63–69 | DOI | – |
| UAK Araştırma Alanları |
Geometri
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| Özet |
| In (n+ 1)-dimensional Euclidean space E n+ 1, harmonic curvatures and focal curvatures of a non-degenerate curve were defined by Özdamar and Hacisalihoglu in [7] and by Uribe-Vargas in [9], respectively. In this paper, we investigate the relations between the harmonic curvatures of a non-degenerate curve and the focal curvatures of tangent indicatrix of the curve. Also we give the relationship between the Frenet apparatus (vectors and the curvature functions) of a curve α in En+ 1 and the Frenet apparatus of tangent indicatrix αT of the curve α. In the main theorem of the paper, we give a characterization for a curve to be a (n-1)-spherical curve in Sn by using focal curvatures of the curve. Furtermore we give that harmonic curvature of the curve is focal curvature of the tangent indicatrix. |
| Anahtar Kelimeler |
| Harmonic curvature | focal curvature | spherical curve | generalized helix | tangent indicatrix |