On isometry groups of gradient Ricci solitons

TL;DR

This paper investigates the symmetry properties of gradient Ricci solitons by estimating the dimension of their isometry groups and analyzing the manifold structure when this maximum is achieved.

Contribution

It provides a new estimate for the dimension of the Lie algebra of Killing vector fields on irreducible non-trivial gradient Ricci solitons and explores the manifold's structure at maximal symmetry.

Findings

Dimension estimate for Killing vector fields

Structural characterization at maximal symmetry

Implications for local and global geometry

Abstract

We give a result estimating the dimension of the Lie algebra of Killing vector fields on an irreducible non-trivial gradient Ricci soliton. Then we study the structure of this manifold when the maximal dimension is attained. There are local and global implications.