Analysis identifies Ricci solitons and their flows in Poincaré space, suggesting broad applicability.
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 Hⁿ. We obtain some nice properties of the soliton about their geodesic flows.
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Bousso et al. (2025) studied this question.
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