Kaluza–Klein type Ricci solitons on unit tangent sphere bundles

We consider g-natural pseudo-Riemannian metrics of Kaluza–Klein type on the unit tangent sphere bundle of a Riemannian manifold of constant sectional curvature and give necessary and sufficient conditions for these metrics to give rise to a Ricci soliton. On the one hand, we 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. On the other hand, while Ricci solitons determined by tangential lifts remain trivial in arbitrary dimension, horizontal lifts of vector fields related to the geometry of the base manifold (namely, homothetic vector fields) produce nontrivial Ricci solitons metrics of Kaluza–Klein type. Gradient Ricci solitons of Kaluza–Klein type are also completely characterized.