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, gS ), 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 gDS or a Mus–Sasaki metric gSF . Lastly, we conclude this article by providing insightful examples of f-harmonic vector fields in the context of the Heisenberg group.