Generalized Ricci Solitons on Three-Dimensional Lorentzian Walker Manifolds

In this paper, we characterize the generalized Ricci soliton equation on the threedimensional Lorentzian Walker manifolds. We prove that every generalized Ricci soliton with C, beta, mu not equal 0 on a three-dimensional Lorentzian Walker manifold is steady. Moreover, non-trivial solutions for strictly Lorentzian Walker manifolds are derived. Finally, we give some conditions on the defining function f under which a generalized Ricci soliton on a three-dimensional Lorentzian Walker manifold to be gradient.