We study Lorentzian manifolds $(M,g)$ of dimension $n\ge 4$, equipped with a maximally twisting shearfree null vector field p, for which the leaf space $S=M/\{\exp t\mathrm{p}\}$ is a smooth manifold. If $n=2k$, the quotient $S=M/\{\exp t\mathrm{p}\}$ is naturally equipped with a subconformal structure of contact type and, in the most interesting cases, it is a regular Sasaki manifold projecting onto a quantisable Kähler manifold of real dimension $2k-2$. Going backwards through this line of ideas, for any quantisable Kähler manifold with associated Sasaki manifold S, we give the local description of all Lorentzian metrics g on the total spaces M of A-bundles $\pi :M\to S$, $A=S^1,\mathbb{R}$, such that the generator of the group action is a maximally twisting shearfree g-null vector field p. We also prove that on any such Lorentzian manifold $(M,g)$ there exists a non-trivial generalised electromagnetic plane wave having p as propagating direction field, a result that can be considered as a generalisation of the classical 4-dimensional Robinson Theorem. We finally construct a 2-parametric family of Einstein metrics on a trivial bundle $M=\mathbb{R}\times S$ for any prescribed value of the Einstein constant. If $\dim M=4$, the Ricci flat metrics obtained in this way are the well-known Taub-NUT metrics.

我们研究洛伦兹流形 $（\mathrm{中号}，G）$ 尺寸 $ñ\ge 4$，配备了最大扭曲的无切零向量场p，其叶空间 $\mathrm{小号}=\mathrm{中号}/\{\mathrm{经验值}Ť\mathrm{p}\}$是光滑的流形。如果$ñ=2ķ$，商 $\mathrm{小号}=\mathrm{中号}/\{\mathrm{经验值}Ť\mathrm{p}\}$ 自然地配备有接触型的亚共形结构，在最有趣的情况下，它是一个常规的Sasaki流形，投射到可实数的可量化Kähler流形上 $2ķ-2$。通过这条线的思想倒退，对于任何quantisable凯勒歧管与相关佐佐木总管小号，我们给所有洛伦兹指标局部描述摹总空间的中号的一个-bundles$\pi ：\mathrm{中号}\to \mathrm{小号}$， $\mathrm{一种}={\mathrm{小号}}^{\mathrm{1个}}，\mathbb{[R}$，使得群作用的生成器是最大扭曲的无剪切g-零矢量场p。我们还证明，在任何此类洛伦兹流形上$（\mathrm{中号}，G）$存在一个以p为传播方向场的非平凡广义电磁平面波，这一结果可以看作是经典4维罗宾逊定理的推广。我们最终在平凡的捆绑中构造了一个2参数爱因斯坦度量标准族$\mathrm{中号}=\mathbb{[R}\times \mathrm{小号}$对于爱因斯坦常数的任何规定值。如果$\mathrm{暗淡}\mathrm{中号}=4$，以此方式获得的Ricci平面度量是著名的Taub-NUT度量。