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

Mohd. Danish Siddiqi; Mehmet Akif Akyol

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arXiv · 2004.14124

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

Mohd. Danish Siddiqi·Mehmet Akif Akyol

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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.

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BibTeX RIS

Mohd. Danish Siddiqi, Mehmet Akif Akyol. 2020-04-23. $\eta$-Ricci-Yamabe Soliton on Riemannian Submersions from Riemannian manifolds. https://arxiv.org/abs/2004.14124

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