Some characterizations for compact hyperbolic Ricci solitons admitting 2-conformal vector fields

In this paper, we find a set of structural equations for hyperbolic Ricci solitons admitting 2-conformal vector fields, which extends similar results for Ricci solitons. As a result of these equations, we obtain an integral formula for the case when the underlying manifold is compact, indicating that a non-trivial compact hyperbolic Ricci soliton with 2-conformal potential vector field is isometric to Euclidean sphere. Also, it will be shown that such manifolds either have constant scalar curvature or their associated vector fields are conformal. Furthermore, we use the Hodge-de Rham decomposition theorem to establish a link with 2-conformal vector fields associated with a hyperbolic Ricci soliton.