On a classification of the quasi Yamabe gradient solitons

Abstract

In this paper, we introduce the concept of quasi Yamabe gradient solitons, which generalizes the concept of Yamabe gradient solitons. By using some ideas in [7,8], we prove that $n$-dimensional $(n\ge 3)$ complete quasi Yamabe gradient solitons with vanishing Weyl curvature tensor and positive sectional curvature must be rotationally symmetric. We also prove that any compact quasi Yamabe gradient solitons are of constant scalar curvature.

11 pages

References in corpus (4)

• The classification of locally conformally flat Yamabe solitons
• Uniqueness of gradient Ricci solitons
• On four-dimensional anti-self-dual gradient Ricci solitons
• On Bach flat warped product Einstein manifolds

Cited by in corpus (1)

• On the geometry of gradient Einstein-type manifolds