On warped product gradient $\eta$-Ricci solitons

Adara M. Blaga

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arXiv · 1705.04092

On warped product gradient $\eta$-Ricci solitons

Adara M. Blaga

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Abstract

If the potential vector field of an $\eta$-Ricci soliton is of gradient type, using Bochner formula, we derive from the soliton equation a Laplacian equation satisfied by the potential function $f$. In a particular case of irrotational potential vector field we prove that the soliton is completely determined by $f$. We give a way to construct a gradient $\eta$-Ricci soliton on a warped product manifold and show that if the base manifold is oriented, compact and of constant scalar curvature, the soliton on the product manifold gives a lower bound for its scalar curvature.

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BibTeX RIS

Adara M. Blaga. 2017-05-11. On warped product gradient $\eta$-Ricci solitons. https://arxiv.org/abs/1705.04092

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