On hyperbolic Ricci solitons

This article explores the idea of hyperbolic Ricci soliton. A hyperbolic Ricci soliton is a Riemannian manifold 1 equipped with a smooth vector field with real constants and fulfilling Ric ++ 2 () =. Also, hyperbolic Ricci solitons provide a comparable solution to hyperbolic Ricci flow. Then, we continue to lay the foundation of hyperbolic Ricci soliton and give some geometric aspects of this concept. Hyperbolic Ricci solitons with special potential vector fields will be studied. Finally, we examine the existence of this new structure on Poincare's half plane.