@article{article_573919, title={Harmonic Aspects in an $\eta$-Ricci Soliton}, journal={International Electronic Journal of Geometry}, volume={13}, pages={41–49}, year={2020}, DOI={10.36890/iejg.573919}, author={Blaga, Adara-monica}, keywords={gradient Ricci solitons,Schrödinger-Ricci equation,harmonic form}, abstract={<p>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. </p> <p> <br /> </p>}, number={1}, publisher={Kazım İlarslan}