Harmonic Aspects in an $eta$-Ricci Soliton

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International Electronic Journal of Geometry
Volume:13 Issue:1
Harmonic Aspects in an $eta$-Ricci Soliton

Harmonic Aspects in an $eta$-Ricci Soliton

Pages : 41-49

View : 51 | Download : 10

Publication Date : 2020-01-30

Article Type : Research Paper

Abstract :We characterize the $\eta$-Ricci solitons $insert ignore into journalissuearticles values(g,\xi,\lambda,\mu);$ 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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