Constant Mean Curvature Surfaces Along a Spacelike Curve

Abstract

We construct constant mean curvature surfaces along a given spacelike curve in 3 dimensional Minkowski space. We parametrically present these surfaces using the famous Frenet frame of the curve in question. We give the sufficient conditions for the so called marching scale functions, which are the coefficients of the Frenet frame fields. We show that it is possible to obtain such surfaces for any given spacelike curve. Finally, the validity of the presented method is supported with illustrative examples.