We already have the concept of isotropicity of a minimal surface in a Riemannian 4-manifold and a space-like or time-like surface in a neutral 4-manifold with zero mean curvature vector. In this paper, based on the understanding of it, we define and study isotropicity of a space-like or time-like surface in a Lorentzian 4-manifold N with zero mean curvature vector. If the surface is space-like, then the isotropicity means either the surface has light-like or zero second fundamental form or it is an analogue of complex curves in Kähler surfaces. In addition, if N is a space form, then the isotropicity means that the surface has both the properties. If the surface is time-like and if N is a space form, then the isotropicity means that the surface is totally geodesic.

我们已经有了黎曼 4 流形中最小曲面的各向同性的概念，以及具有零平均曲率向量的中性 4 流形中的类空间或类时间曲面。本文基于对它的理解，定义和研究了平均曲率向量为零的洛伦兹4-流形N中类空间或类时间表面的各向同性。如果表面是类空间的，那么各向同性意味着该表面要么具有类光或零秒基本形式，要么它类似于 Kähler 表面中的复杂曲线。另外，如果N是空间形式，那么各向同性意味着表面同时具有这两种性质。如果表面是类时间的并且如果N是一种空间形式，那么各向同性意味着表面是完全测地线的。