Kaluza–Klein type Ricci solitons on unit tangent sphere bundles

On $g$-natural conformal vector fields on unit tangent bundles

“…For example, in the framework of the Riemannian geometry of tangent bundles, Killing and conformal vector fields had been classified on tangent bundles of Riemannian manifolds, equipped with the Sasaki metric (see [28] and [29]) and the Cheeger-Gromoll metric (see [8] and [18]), respectively. When the tangent bundle is endowed with an arbitrary g-natural metric, it is not easy to find a full classification of conformal or Killing vector fields, but we can find some partial results on the subject (see [17] for Killing vector fields and [2], [20], [25] for conformal vector fields).…”

Natural Ricci Solitons on Tangent and Unit Tangent Bundles

“…In [2], the authors treated the problem of finding Ricci soliton structures on the unit tangent bundle of a Riemannian manifold, endowed with a pseudo-Riemannian Kaluza-Klein type metric, which is an interesting subclass of the class of g-natural metrics that shares with the Sasaki metric the property of preserving the orthogonality of horizontal and vertical distributions. They obtain a rigidity result in dimension three, showing that there are no nontrivial Ricci solitons among g-natural metrics of Kaluza-Klein type on the unit tangent sphere bundle of any Riemannian surface.…”