Surface Pencil with a Common Line of Curvature in Minkowski 3-Space

Abstract

In this paper, we analyze the problem of constructing a surface pencil from a given spacelike (timelike) line of curvature. Using the Frenet frame of the given line of curvature 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. We illustrate this method by presenting some examples. © 2014, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.