Ricci Solitons on a family of three dimensional Lorentzian Walker manifolds

Abstract

A Ricci soliton is a natural generalization of an Einstein metric. On a pseudo-Riemannian manifold (M, g), it is defined by : $LX g + \r{ho} = {\lambda} g, where X is a smooth vector field on M , LX denotes the Lie derivative in the direction of X, \r{ho} is the Ricci tensor, and {\lambda} is a real constant. In this paper, we establish the existence of non-trivial Ricci solitons on a family of three-dimensional Lorentzian Walker manifolds.