Some characterizations for compact Hyperbolic Ricci solitons admitting 2-Conformal vector fields

Abstract

‎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.