Vanishing Results for the Cotton Tensor on Gradient Quasi-Einstein Solitons

• 作者: Lin Feng WANG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（4）
• 页码范围: 588-596
• 页数: 9页
• 语种: 英文

摘要

In this paper we study on gradient quasi-Einstein solitons with a fourth-order vanishing condition on the Weyl tensor. More precisely,we show that for n ≥ 4,the Cotton tensor of any n-dimensional gradient quasi-Einstein soliton with fourth order f-divergence free Weyl tensor is flat,if the manifold is compact,or noncompact but the potential function satisfies some growth condition. As corollaries,some local characterization results for the quasi-Einstein metrics are derived.