On The Explicit Characterization Of Curves On A (N - 1)-Sphere In Sn
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Dosyalar
Tarih
2013
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Int Electronic Journal Geometry
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In (n+1)-dimensional Euclidean space E-n+(1), harmonic curvatures and focal curvatures of a non-degenerate curve were defined by Ozdamar 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 alpha in E-n (+1) and the Frenet apparatus of tangent indicatrix alpha(T) of the curve alpha. In the main theorem of the paper, we give a characterization for a curve to be a (n-1)-spherical curve in S-n by using focal curvatures of the curve. Furtermore we give that harmonic curvature of the curve is focal curvature of the tangent indicatrix.
Açıklama
Anahtar Kelimeler
Harmonic curvature; focal curvature; spherical curve; generalized helix; tangent indicatrix
Kaynak
International Electronic Journal of Geometry
WoS Q Değeri
N/A
Scopus Q Değeri
Cilt
6
Sayı
2
