# K\"ahler-Ricci flow on horospherical manifold

## TL;DR

This paper demonstrates that the Kähler-Ricci flow on smooth Fano horospherical manifolds converges to a Kähler-Ricci soliton, establishing existence through geometric flow analysis.

## Contribution

It proves the existence of Kähler-Ricci solitons on all smooth Fano horospherical manifolds via flow convergence analysis.

## Key findings

- Renormalized Kähler-Ricci flow converges in Cheeger-Gromov sense.
- Limit of flow is a Kähler-Ricci soliton.
- Existence of solitons on Fano horospherical manifolds established.

## Abstract

In this paper, we prove the existence of a Kahler Ricci soliton on any smooth Fano horospherical manifold by a study of the Kahler-Ricci flow. Indeed, we prove that the renormalized Kahler Ricci flow converges in the sense of Cheeger Gromov and that this limit is a Kahler-Ricci soliton.