Properties of Bertrand curves in dual space

International Journal of Physical Sciences

İlkay ARSLAN Gܹ 

关键词: Bertrand curves;    involute-evolute curves;    dual space.;   

DOI  :  10.5897/IJPS2013.4067

学科分类：物理（综合）

来源: Academic Journals

【 摘 要 】

Starting from ideas and results given by Özkaldi, İlarslan and Yaylı in (2009), in this paper we investigate Bertrand curves in three dimensional dual space D3. We obtain the necessary characterizations of these curves in dual space D3. As a result, we find that the distance between two Bertrand curves and the dual angle between their tangent vectors are constant. Also, well known characteristic property of Bertrand curve in Euclid space E3which is the linear relation between its curvature and torsion is satisfied in dual space asλ.κ(S) + μ.τ(S) = 1.We show that involute curves, which are the curves whose tangent vectors are perpendicular, of a curve constitute Bertrand pair curves.

【 授权许可】

CC BY