Ricci solitons as submanifolds of complex hyperbolic spaces

TL;DR

This paper classifies and analyzes the geometry of Lie subgroups that form Ricci solitons as submanifolds within complex hyperbolic spaces, extending understanding of homogeneous Ricci solitons in these settings.

Contribution

It provides a classification and geometric analysis of Lie subgroups with Ricci soliton metrics in complex hyperbolic spaces, a new insight into their structure.

Findings

Classification of Lie subgroups with Ricci soliton metrics in complex hyperbolic spaces

Detailed geometric properties of these subgroups

Extension of known results to complex hyperbolic symmetric spaces

Abstract

Any homogeneous expanding Ricci soliton is known to be isometric to a Lie subgroup of the solvable part of the Iwasawa decomposition associated with a symmetric space of non-compact type, with the metric induced as a submanifold. In this paper, we classify and analyze the geometry of such Lie subgroups with Ricci soliton induced metric when the symmetric spaces are complex hyperbolic spaces.