Classification of arbitrary-potential hyperbolic Ricci solitons on the Sasaki unit tangent bundle

Classify hyperbolic Ricci solitons for arbitrary smooth potential vector fields on the unit tangent bundle T^1S_a of the hyperbolic strip, beyond the established cases of Killing fields, left-invariant fields, and θ-invariant fields with conformal projection.

Background

The paper studies hyperbolic Ricci solitons satisfying Ric^S + λ L_X g^S + 1/2 L_X(L_X g^S) = μ g^S on the unit tangent bundle T^1S_a equipped with the Sasaki metric. It proves non-existence for Killing potentials, left-invariant potentials, and θ-invariant potentials whose projection to the hyperbolic strip is conformal.

For a general θ-invariant potential, the authors reduce the problem to a system of equations on the base strip involving the projected vector field V and a one-form β. They do not solve this system, and the nonlinear dependence on the potential prevents the averaging argument used for ordinary Ricci solitons from extending to arbitrary potentials.