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Ricci solitons of the Sol3 Lie group
  • BELARBI LAKEHAL
BELARBI LAKEHAL
Universite Abdelhamid Ibn Badis de Mostaganem
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Abstract

In this work we consider the three-dimensional solvable Lie group denoted by $Sol_{3}$, equipped with any left-invariant metric, either Lorentzian or Riemannian. The existence of non-trivial (i.e., not Einstein) Ricci solitons on both Lorentzian and Riemannian three-dimensional solvable Lie group $Sol_{3}$ is proved. Moreover, we show that they are not gradient Ricci solitons.