Ricci–Yamabe solitons along Riemannian maps

The main aim of this paper is to study a Riemannian map between Riemannian manifolds admitting a Ricci–Yamabe soliton. Here, we deal with a Riemannian map whose total manifold or base manifold admits a Ricci–Yamabe soliton and obtain some necessary conditions for which [Formula: see text], [Formula: see text] and [Formula: see text] admit a Ricci–Yamabe soliton or Einstein.