Riemann zero mean curvature examples in Lorentz–Minkowski space

Abstract

Riemann zero mean curvature examples in the Lorentz–Minkowski space are surfaces with zero mean curvature foliated by circles contained in parallel planes. In contrast to the Euclidean case, this family of surfaces presents new and rich features because of the variety of types of circles. In this paper, we give a geometric description of these examples when the circles are contained in spacelike planes and timelike planes.