Communications of the
Korean Mathematical Society CKMS

In this paper, we study Riemannian submersions whose total manifold admits $h$-almost Ricci-Yamabe soliton. We characterize the fibers of the submersion and see under what conditions the fibers form $h$-almost Ricci-Yamabe soliton. Moreover, we find the necessary condition for the base manifold to be an $h$-almost Ricci-Yamabe soliton and Einstein manifold. Later, we compute scalar curvature of the total manifold and using this we find the necessary condition for $h$-almost Yamabe solition to be shrinking, expanding and steady. At the end, we give a non-trivial example.

Keywords: $h$-almost Ricci-Yamabe soliton, Ricci flat manifold, Riemannian submersion

MSC numbers: 53C12, 53C25, 53C40