Natural lifts and the geodesic sprays for the spherical indicatrıces of the mannheim partner curves in

International Journal of Physical Sciences

Suuml¹ 

关键词: Mannheim curve;    natural lift of spherical indicatrix curve;    geodesic spray;    geodesic curvatures.;   

DOI  :  10.5897/IJPS12.259

学科分类：物理（综合）

来源: Academic Journals

【 摘 要 】

In this paper, we investigated the natural lifts and curvatures of the spherical indicatrices of the Mannheim partner curves in. Firstly, it is shown that the Darboux vector of Mannheim curve and tangent vector of the Mannheim partners should be linearly dependent. Secondly, the relations among the geodesic curvatures and arc-lengths with respect toandof the fixed pole curveand the spherical indicatrix curvesgenerated by the unit vectoroccured depending on the Frenet frameof Mannheim partner curveonhave been obtained and finally, the condition being that the natural lifts of the spherical indicatrix curves of the Mannheim partner curveare an integral curve of geodesic spray has been expressed depending on Mannheim curve.

【 授权许可】

CC BY