Harmonic Aspects in an -Ricci Soliton

Abstract

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