Abstract

Starting from ideas and results given by Özkaldi, Ä°larslan 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 E³ which is the linear relation between its curvature and torsion is satisfied in dual space as λ.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.

Key words: Bertrand curves, involute-evolute curves, dual space.

2000 Mathematics Subject Classification: 53A04 , 53A25 , 53A40.