WEAKLY-EINSTEIN CONDITIONS OVER LOCALLY CONFORMALLY FLAT LORENTZIAN THREE-MANIFOLDS

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.

Automated summary

This paper classifies Lorentzian manifolds of dimension n = 3 that satisfy the Codazzi equation, and applies this classification to characterize three-dimensional weakly-Einstein Lorentzian manifolds in the conformal class of flat metrics.