Harmonic Aspects in an $\eta$-Ricci Soliton

Year 2020, Volume: 13 Issue: 1, 41 - 49, 30.01.2020

Adara-monica Blaga

https://doi.org/10.36890/iejg.573919

Cited By: 4

Abstract

We characterize the $\eta$-Ricci solitons $(g,\xi,\lambda,\mu)$ for the special cases when the $1$-form $\eta$, which is the $g$-dual of $\xi$, is a harmonic or a Schr\"{o}dinger-Ricci harmonic form. We also provide necessary and sufficient conditions for $\eta$ to be a solution of the Schr\"{o}dinger-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-Weitzenb\"{o}ck techniques, we formulate some more conclusions for the case of gradient solitons and deduce topological properties of the manifold and its universal covering.

Keywords

gradient Ricci solitons, Schrödinger-Ricci equation, harmonic form

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