Exploring the Properties of f-Harmonic Vector Fields

In this paper, our objective is to explore specific characteristics of fharmonic vector fields.Firstly, we delve into the properties of an f -harmonic Killing vector field when it acts as an f -harmonic map between a Riemannian manifold denoted as (M, g) and its tangent bundle (T M, g S ), which is equipped with the Sasaki metric.We emphasize this investigation when (M, g) takes the form of either an Einstein manifold or a space form.Secondly, we study the traits exhibited by an f -harmonic vector field between a Riemannian manifold (M, g) and its tangent bundle T M equipped with either a deformed Sasaki metric g DS or a Mus-Sasaki metric g SF .Lastly, we conclude this article by providing insightful examples of f -harmonic vector fields in the context of the Heisenberg group.