Surface Pencil With a Common Timelike Adjoint Curve

Abstract

The adjoint curve of a Frenet curve r=r(s) is defined as the unit speed curve tan-gent to the principal normal vector field of r. We show that the adjoint curve of a spacelike curve with timelike binormal is a timelike curve. We obtain some relationships between a Frenet curve and its adjoint in Minkowski 3-space. For a given spacelike curve with timelike binormal, we obtain conditions on surfaces that possess the adjoint curve as a common asymptotic, geodesic or curvature line in Minkowski 3-space. We also give examples confirming our theory. © 2024, Palestine Polytechnic University. All rights reserved.