Generalized Lorentz Ricci solitons on -dimensional Lie groups associated to Bott connection

Abstract

In this paper, we investigate which one of the non-isometric left-invariant Lorentz metrics g on 3-dimensional Lie groups satisfies the generalized Ricci soliton equa- tion aRic^B [g] + b/2 L^B_X g + cX♭ ⊗ X♭ = λg associated to the Bott connection ∇B , here X is a vector field and λ, a, b, c are real constants such that c̸ = 0. A com- plete classification of this structure on 3-dimensional Lorentzian Lie groups will be presented