$\eta$-Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds

Abstract

In this research article, we establish the geometrical bearing on Riemannian submersions in terms of $\eta$-Ricci-Yamabe Soliton with the potential field and giving the classification of any fiber of Riemannian submersion is an $\eta$-Ricci-Yamabe soliton, $\eta$-Ricci soliton and $\eta$-Yamabe soliton. We also discuss the various conditions for which the target manifold of Riemannian submersion is an $\eta$-Ricci-Yamabe soliton, $\eta$-Ricci soliton, $\eta$-Yamabe soliton and quasi-Yamabe soliton. In a particular case when the potential filed $V$ of the $\eta$-Ricci-Yamabe soliton is of gradient type, we derive a Laplacian equation and providing some examples of an $\eta$-Ricci-Yamabe soliton on a Riemannian submersion. Finally, we study harmonic aspect of $\eta$-Ricci-Yamabe soliton on Riemannian submersions and mention geometrical and physical effects of Ricci-Yamabe solitons.

16 pages. arXiv admin note: text overlap with arXiv:1404.2385, arXiv:1311.1676 by other authors