
arXiv: 1108.6177
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 $(n\geq3)$ 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
Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics
Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics
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