The structure of the Ricci tensor on locally homogeneous Lorentzian gradient Ricci solitons

Abstract

We describe the structure of the Ricci tensor on a locally homogeneous Lorentzian gradient Ricci soliton. In the non-steady case, we show the soliton is rigid in dimensions three and four. In the steady case, we give a complete classification in dimension three.

19 pages. Updated version

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