We present three large classes of examples of conformal structures for which the equations for the Fefferman-Graham ambient metric to be Ricci-flat are linear PDEs, which we solve explicitly. These explicit solutions enable us to discuss the holonomy of the corresponding ambient metrics. Our examples include conformal pp-waves and, more importantly, conformal structures that are defined by generic rank 2 and 3 distributions in respective dimensions 5 and 6. The corresponding explicit Fefferman-Graham ambient metrics provide a large class of metrics with holonomy equal to the exceptional non-compact Lie group $\mathbf{G}_2$ as well as ambient metrics with holonomy contained in $\mathbf{Spin}(4,3)$.

中文翻译：

---

显式环境指标和完整度

我们提出了三大类共形结构的例子，其中 Fefferman-Graham 环境度量为 Ricci-flat 的方程是线性偏微分方程，我们明确求解。这些明确的解决方案使我们能够讨论相应环境指标的整体性。我们的例子包括共形 pp 波，更重要的是，共形结构由各自维度 5 和 6 中的通用等级 2 和 3 分布定义。相应的显式 Fefferman-Graham 环境度量提供了一大类度量，其完整性等于特殊的非紧李群 $\mathbf{G}_2$ 以及包含在 $\mathbf{Spin}(4,3)$ 中的具有完整度的环境度量。