ON THE EXPLICIT CHARACTERIZATION OF CURVES ON A (n - 1)-SPHERE IN Sn
[ X ]
Date
2013
Journal Title
Journal ISSN
Volume Title
Publisher
Int Electronic Journal Geometry
Access Rights
info:eu-repo/semantics/closedAccess
Abstract
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.
Description
Keywords
Harmonic curvature; focal curvature; spherical curve; generalized helix; tangent indicatrix
Journal or Series
International Electronic Journal of Geometry
WoS Q Value
N/A
Scopus Q Value
Volume
6
Issue
2
