arXiv:1305.0341v1 [math.DG] 2 May 2013 SURFACE PENCIL WITH A COMMON LINE OF CURVATURE IN MINKOWSKI 3-SPACE Evren ERG ¨ UN, Ergin BAYRAM, Emin KASAP Ondokuz Mayıs University, Faculty of Arts and Sciences, Department of Mathematics, Samsun TURKEY eergun@omu.edu.tr, erginbayram@yahoo.com, kasape@omu.edu.tr In this paper, we analyze the problem of constructing a surface pencil from a given spacelike (timelike) line of curvature. By using the Frenet frame of the given curve in Minkowski 3-space, we express the surface pencil as a linear combination of this frame and derive the necessary and sufficient conditions for the coefficients to satisfy the line of curvature requirement. To illustrate the method some examples showing members of the surface pencil with their line of curvature are given. Keywords: Minkowski space, Line of curvature, Surface pencil. 2000 Mathematics Subject Classification: 53B30, 51B20, 53C50. Short Title: Surfaces with common line of curvature in R 3 1 1 Abstract