Ricci Solitons on the Poincaré upper half plane

Abstract: In this paper, we characterize the Ricci soliton equations on the Poincar\'e upper half plane . First we classify all Ricci soliton and Ricci Bourguignon soliton in the half plane of Poincar\'e and after we generalize those equations in $\mathbb{H}<sup>n$. We obtain some nice properties of the soliton about their geodesic flows.