Zero mean curvature surfaces in \(\mathrm{L}^3\) containing a light-like line (Q694691)

In this research note, the authors provide a few interesting examples of surfaces for which the set of singular points (where the induced metric degenerates) consists of a light-like line. They introduce an important tool, called characteristic of a zero mean curvature surface along a singular light-like line. It is shown that, for specific cases, there exists a real analytic zero mean curvature surface in the Lorenz-(Minkowski) 3-space containing a light-like line segment with certain properties. This result is proven by providing several examples. Although brief, this communication is of genuine novelty and outstanding scientific value.