Lorentz Ricci solitons of 4-dimensional non-Abelian nilpotent Lie groups

Abstract

The goal of this paper is to investigate which one of thenon-isometric left invariant Lorentz metrics on 4-dimensional nilpotent Lie groups H3 × R and G4 satisfy in Ricci Soliton equation. Among the left-invariant Lorentzian metrics on H3 × R, g + λ is a shrinking while g + λ and gµ are expanding and also g 1 0 , g 2 0 , g 3 0 have Ricci solitons. We exhibit among the non-isometric left invariant Lorentz metric on the group G4 only g λ 1 , g λ 2 have Lorentz Ricci solitons and g λ 2 is a shrinking.