Complete gradient Ricci solitons with zero radial Weyl curvature

TL;DR

This paper classifies complete gradient Ricci solitons with zero radial Weyl curvature for dimensions four and higher, expanding understanding of their geometric structure.

Contribution

It provides a complete classification of such solitons under the specified curvature condition for dimensions n ≥ 4.

Findings

Complete classification achieved for n ≥ 4

Identifies geometric properties under zero radial Weyl curvature

Advances understanding of Ricci solitons with special curvature conditions

Abstract

In this paper, we study the complete gradient Ricci solitons $(M^n, g,f)$ with zero radial Weyl curvature, which means that the interior product of $\nabla f$ with the Weyl tensor $W$ is zero, i.e., $i_{\nabla f}W=0$. We classify completely the complete gradient Ricci solitons with zero radial Weyl curvature for the dimension $n\geq 4$.