Affine Ricci solitons of three-dimensional Lorentzian Lie groups

Abstract

In this paper, we classify affine Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections and perturbed canonical connections and perturbed Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure.

Left-invariant Riemann solitons of three-dimensional Lorentzian Lie groups

“…In [4], Calvaruso completely classify three-dimensional homogeneous manifolds equipped with Einsteinlike metrics. In [8], we classify affine Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections and perturbed canonical connections and perturbed Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure. In this note, we completely classify left-invariant Riemann solitons on three-dimensional Lorentzian Lie groups.…”