Some uniqueness results for Ricci solitons

Abstract

We investigate the relationship between Ricci soliton structures and homothetic vector fields, especially Killing vector fields. More precisely, we present some characterizations for Ricci solitons endowed with Killing vector fields of constant norm as well as homothetic vector fields. In particular, we relate different Ricci soliton structures on a Riemannian manifolds in order to deduce some uniqueness results.