Several geometric properties of complete spacelike submanifolds, with codimension at least two, in a Brinkmann spacetime are shown from natural assumptions involving the mean curvature vector field H of the spacelike submanifold. Especially, we get sufficient conditions that assure that a spacelike submanifold is contained in a leaf of the foliation of the Brinkmann spacetime defined by the orthogonal vectors to the parallel lightlike vector field. When this vector field is the gradient of a smooth function, a characterization of arbitrary codimension spacelike submanifolds contained in a leaf of this foliation is given. In the case of plane fronted wave spacetimes, relevant examples of Brinkmann spacetimes that generalize pp-waves spacetimes, several uniqueness results for codimension two spacelike submanifolds are obtained. In particular, it is proven that any compact codimension two spacelike submanifold with H = 0 in a plane fronted spacetime wave must be a (totally geodesic) front of wave.

布林克曼时空中的完整类空子流形的几个几何性质，至少有两个余维，从涉及平均曲率向量场H 的自然假设中显示的空间子流形。特别是，我们得到了足够的条件，以确保在 Brinkmann 时空叶理的叶子中包含类空间子流形，该叶子由平行的类光向量场的正交向量定义。当该向量场是平滑函数的梯度时，给出了包含在该叶面的叶子中的任意余维类空间子流形的表征。在平面前波时空的情况下，Brinkmann 时空的相关例子推广了 pp 波时空，获得了两个类空间子流形的余维唯一性结果。特别是，它证明了在平面前时空波中任何具有H = 0 的紧凑共维二类空间子流形必须是（完全测地线的）波前。