Ricci Solitons on the Poincar\'e upper half plane

TL;DR

This paper classifies Ricci and Ricci Bourguignon solitons on the Poincaré upper half plane and generalizes the equations to higher dimensions, analyzing their geodesic flow properties.

Contribution

It provides a complete classification of Ricci solitons on the Poincaré upper half plane and extends the analysis to hyperbolic spaces of higher dimensions.

Findings

Classification of Ricci solitons on the Poincaré upper half plane

Generalization of soliton equations to  hyperbolic space

Analysis of geodesic flow properties of the solitons

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 $\mathbb{H}^n$. We obtain some nice properties of the soliton about their geodesic flows.