From Infinitesimal Harmonic Transformations to Ricci Solitons

TL;DR

This paper surveys the geometry of Ricci solitons, highlighting their connection to infinitesimal harmonic transformations, and discusses their role as natural generalizations of Einstein metrics.

Contribution

It demonstrates how Ricci solitons can be understood through the theory of infinitesimal harmonic transformations, providing a new perspective on their geometric properties.

Findings

Ricci soliton vector fields are infinitesimal harmonic transformations

Ricci solitons generalize Einstein metrics

Survey of Ricci solitons as applications of harmonic transformation theory

Abstract

The concept of the Ricci soliton was introduced by Hamilton. Ricci soliton is defined by vector field and it's a natural generalization of Einstein metric. We have shown earlier that the vector field of Ricci soliton is an infinitesimal harmonic transformation. In our paper, we survey Ricci solitons geometry as an application of the theory of infinitesimal harmonic transformations.