Ricci bi-conformal vector fields on four-dimensional Lorentzian Damek-Ricci spaces

Abstract

In this paper, we obtain all Ricci bi-conformal vector fields on the four-dimensional Lorentzian Damek-Ricci spaces and we show that four-dimensional Lorentzian Damek-Ricci spaces have not nontrivial Ricci bi-conformal vector fields as gradient vector filed. Also, we determine which of them are Killing vector fields.