- International Electronic Journal of Geometry
- Vol: 13 Issue: 1
- Harmonic Aspects in an $\eta$-Ricci Soliton
Harmonic Aspects in an $\eta$-Ricci Soliton
Authors : Adara-monica Blaga
Pages : 41-49
Doi:10.36890/iejg.573919
View : 7 | Download : 3
Publication Date : 2020-01-30
Article Type : Research
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