Ricci and Yamabe solitons on second-order symmetric, and plane wave 4-dimensional Lorentzian manifolds

摘要

We show that a proper second-order symmetric spacetime, and four-dimensional Lorentzian plane wave manifolds admit different vector fields resulting in expanding, steady and shrinking Ricci and Yamabe solitons. Moreover, it is proved that those Ricci and Yamabe solitons are gradient only in the steady case.