Some Remarks on Riemannian Submersions Admitting An Almost Yamabe Soliton

Abstract

In this paper, we study the Riemannian submersions $\pi:M\rightarrow B$ whose total manifolds admit an almost Yamabe soliton. Here, we give some necessary conditions for which any fiber of $\pi$ or $B$ are almost Yamabe soliton or Yamabe soliton. Also, we calculate the scalar curvatures of any fiber or $B$ and using them, we present the relations between the scalar curvatures of them and obtain some characterizations of such a soliton (that is, shrinking, steady or expanding).