Spacelike Zero Mean Curvature Surfaces in $${\mathbb {L}}^{4}$$

Abstract

We present new explicit parametrizations of spacelike zero mean curvature surfaces in four-dimensional Lorentz–Minkowski space $${\mathbb {L}}^{4}$$. The surfaces are the solutions of the Bjorling problem whose core curve is a circle and a helix and the tangent planes are expressed in terms of trigonometric functions.