On Rectifying Dual Space Curves Ahmet Y ¨ UCESAN, Nihat AYYILDIZ, and A. Ceylan C ¸ ¨ OKEN S¨ uleyman Demirel University Department of Mathematics 32260 Isparta — Turkey yucesan@fef.sdu.edu.tr ayyildiz@fef.sdu.edu.tr ceylan@fef.sdu.edu.tr Received: October 23, 2006 Accepted: April 26, 2007 ABSTRACT We give some characterizations of the rectifying curves in the dual space and show that rectifying dual space curves can be stated with the aid of dual unit spherical curves. Thus, we have a link between rectifying dual space curves and classical surfaces in the Euclidean three-space. Key words: dual space, rectifying dual space curve, Frenet formulae, dual Darboux vector. 2000 Mathematics Subject Classification: 53A04, 53A25, 53A40. Introduction In the Euclidean three-space R 3 , lines combined with one of their two directions can be represented by unit dual vectors over the ring of dual numbers. The most important properties of real vector analysis are valid for the dual vectors. The oriented lines in R 3 are in one-to-one correspondence with the points of a dual unit sphere. A dual point on dual unit sphere in D 3 corresponds to a line in R 3 and two different points on D 3 represent two skew-lines in R 3 in general. A differentiable curve on dual unit sphere in D 3 represents a ruled surface in R 3 (see [4, 5]). A curve in R 3 whose position vector always lies in its rectifying plane is called a rectifying curve. A useful method of determining rectifying curves in the Euclidean three-space R 3 has been developed by Chen [1]. He shows that it can be possible to determine completely all rectifying curves in R 3 . Rev. Mat. Complut. 20 (2007), no. 2, 497–506 497 ISSN: 1139-1138