# Gradient Ricci soliton

From Diffgeom

*This article defines a property that makes sense for a Riemannian metric over a differential manifold*

## Definition

### Given data

A differential manifold and a Riemannian metric on .

### Definition part

A **gradient Ricci soliton** is a Ricci soliton for which the corresponding complete vector field is the gradient of a potential function.