Gradient Shrinking Solitons with Vanishing Weyl Tensor

TL;DR

This paper provides a local pinching estimate and a complete classification of gradient shrinking solitons with vanishing Weyl tensor, advancing understanding of their geometric structure.

Contribution

It introduces a local Hamilton-Ivey type pinching estimate and fully classifies gradient shrinking solitons with vanishing Weyl tensor.

Findings

Established a local pinching estimate for these solitons

Provided a complete classification of the solitons with vanishing Weyl tensor

Enhanced understanding of the geometric properties of such solitons

Abstract

In this paper, we will give a local version of the Hamilton-Ivey type pinching estimate of the gradient shrinking soliton with vanishing Weyl tensor, and then give a complete classification on gradient shrinking solitons with vanishing Weyl tensor.