On a compact Einstein-type manifolds with Riemannian foliations

Abstract

We investigate a compact Einstein-type manifold whose potential vector field generates a Riemannian foliation. In particular, we prove necessary conditions for such a manifold to be taut and to have a splitting property. Additionally, some properties of taut Riemannian foliations on a compact almost Ricci solitons and a compact Einstein manifolds are provided.