Riemannian submersions whose total manifold admits $h$-almost Ricci-Yamabe soliton
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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.
Abstract
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.
참고문헌 (20)
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