On gradient Ricci solitons with constant scalar curvature

TL;DR

This paper investigates gradient Ricci solitons with constant scalar curvature using isoparametric functions, establishing rigidity results and providing a complete classification in certain dimensions, especially for Kaehler manifolds.

Contribution

It introduces new rigidity results for gradient Ricci solitons with constant scalar curvature and classifies specific cases in four and six dimensions, particularly for Kaehler manifolds.

Findings

Rigidity of gradient Ricci solitons under certain Ricci tensor conditions

Complete classification of 4- and 6-dimensional Kaehler gradient Ricci solitons with constant scalar curvature

Conditions satisfied by curvature homogeneous manifolds

Abstract

We use the theory of isoparametric functions to investigate gradient Ricci solitons with constant scalar curvature. We show rigidity of gradient Ricci solitons with constant scalar curvature under some conditions on the Ricci tensor, which are all satisfied if the manifold is curvature homogeneous. This leads to a complete description of four- and six-dimensional Kaehler gradient Ricci solitons with constant scalar curvature.