Commun. Korean Math. Soc. 2024; 39(2): 479-492
Online first article March 28, 2024 Printed April 30, 2024
https://doi.org/10.4134/CKMS.c230203
Copyright © The Korean Mathematical Society.
Mehraj Ahmad Lone, Towseef Ali Wani
National Institute of Technology Srinagar; National Institute of Technology Srinagar
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
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