construction of a surface pencil with a common special surface curve

In this study, we introduce a new type of surface curves called d- type curve. this curve is de ned by the property that the unit darboux vector w 0 of a surface curve r(s) and unit surface normal n along the curve r(s) satisfy the condition d n,w 0 e = constant. we point out that a d-type curve is a geodesic curve or an asymptotic curve in some special cases. then, by using the frenet vectors and parametric representation of a surface pencil as a linear combination of the frenet vectors, we investigate necessary and sufficient condition for a curve to be a d-type curve on a surface pencil. moreover, we introduce some corollaries by considering the d-type curve as a helix, a salkowski curve or a planar curve. finally, we give some examples for the obtained results.