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 ndimensional gradient quasi-Einstein ...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 ndimensional 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.展开更多
文摘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 ndimensional 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.
