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arXiv · 1803.04679

Harmonic aspects in an $η$-Ricci soliton

Adara M. Blaga
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Abstract

We characterize $η$-Ricci solitons $(g,ξ,λ,μ)$ in some special cases when the $1$-form $η$, which is the $g$-dual of $ξ$, is a harmonic or a Schrödinger-Ricci harmonic form. We also provide necessary and sufficient conditions for $η$ to be a solution of the Schrödinger-Ricci equation and point out the relation between the three notions in our context. In particular, we apply these results to a perfect fluid spacetime and using Bochner- Weitzenböck techniques, we formulate some more conclusions for gradient solitons and deduce topological properties of the manifold and its universal covering.

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Adara M. Blaga. 2020-08-23. Harmonic aspects in an $η$-Ricci soliton. https://doi.org/10.36890/iejg.573919

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