论文标题
在均匀的维度上扭曲无效的大地测量学，几乎CR结构和爱因斯坦指标
Twisting non-shearing congruences of null geodesics, almost CR structures, and Einstein metrics in even dimensions
论文作者
论文摘要
我们研究了均超过四个尺寸和洛伦兹的签名的连形歧管的旋转曲折的扭曲的无外侧一致性的几何形状。我们在Weyl张量上给出了扭曲的必要条件，以引起几乎Robinson的结构，也就是说，一致性的屏幕束配备了束复合体结构。在这种情况下，一致性的（局部）叶片空间获得了一个可部分整合的触点，几乎具有正定签名的CR结构。我们为几乎鲁滨逊结构和几乎CR结构以及后者的平坦度提供了进一步的曲率条件。 我们表明，在对Weyl张量的轻度自然假设下，共形类别中的任何度量是对爱因斯坦田间方程的解决方案的任何度量，它决定了一致性的叶片空间上几乎是Cr-Einstein结构。这些指标取决于三个参数，并包括Fefferman-Einstein Metric和Taub-nut-（a）ds ds度量。在不可综合的情况下，我们获得了爱因斯坦田间方程的新解决方案，我们表明，它可以从严格的几乎是Kaehler-Einstein歧管中构造。
We investigate the geometry of a twisting non-shearing congruence of null geodesics on a conformal manifold of even dimension greater than four and Lorentzian signature. We give a necessary and sufficient condition on the Weyl tensor for the twist to induce an almost Robinson structure, that is, the screen bundle of the congruence is equipped with a bundle complex structure. In this case, the (local) leaf space of the congruence acquires a partially integrable contact almost CR structure of positive definite signature. We give further curvature conditions for the integrability of the almost Robinson structure and the almost CR structure, and for the flatness of the latter. We show that under a mild natural assumption on the Weyl tensor, any metric in the conformal class that is a solution to the Einstein field equations determines an almost CR-Einstein structure on the leaf space of the congruence. These metrics depend on three parameters, and include the Fefferman-Einstein metric and Taub-NUT-(A)dS metric in the integrable case. In the non-integrable case, we obtain new solutions to the Einstein field equations, which, we show, can be constructed from strictly almost Kaehler-Einstein manifolds.
