The classical Patterson-Walker construction of a split-signature (pseudo-)Riemannian structure from a given torsion-free affine connection is generalized to a construction of a split-signature conformal structure from a given projective class of connections. A characterization of the induced structures is obtained. We achieve a complete description of Einstein metrics in the conformal class formed by the Patterson-Walker metric. Finally, we describe all symmetries of the conformal Patterson-Walker metric. In both cases we obtain descriptions in terms of geometric data on the original structure.

中文翻译：

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保形帕特森-沃克指标

来自给定无扭仿射连接的分裂特征（伪）黎曼结构的经典 Patterson-Walker 构造被推广为从给定的投影类连接构建分裂特征共形结构。获得诱导结构的表征。我们在由 Patterson-Walker 度量形成的共形类中实现了对爱因斯坦度量的完整描述。最后，我们描述了保形 Patterson-Walker 度量的所有对称性。在这两种情况下，我们都根据原始结构的几何数据获得描述。