We classify the Lorentzian manifolds of dimension n ≥ 3 admitting some diagonalizable operators which satisfy the Codazzi equation. This classification is applied to characterize three-dimensional weakly-Einstein Lorentzian manifolds which fall in the conformal class of the flat metrics.

中文翻译：

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局部共形平坦洛伦兹三流形上的弱爱因斯坦条件

我们对维度n ≥ 3的洛伦兹流形进行分类，允许一些满足 Codazzi 方程的可对角化算子。该分类用于表征属于平面度量的共形类的三维弱爱因斯坦洛伦兹流形。