Generalized Ricci Solitons on Three-Dimensional Lorentzian Walker Manifolds

Abstract

In this paper, we characterize the generalized Ricci soliton equation on the three-dimensional Lorentzian Walker manifolds. We prove that every generalized Ricci soliton with C, beta ,mu ne 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.