The classification of locally conformally flat Yamabe solitons

Details The classification of locally conformally flat Yamabe solitons The classification of locally conformally flat Yamabe solitons

2011-04-12

arxiv.org/abs/1104.2242v2

Mathematics

Differential Geometry

Scientific paper

We provide the classification of locally conformally flat gradient Yamabe solitons with positive sectional curvature. We first show that locally conformally flat gradient Yamabe solitons with positive sectional curvature have to be rotationally symmetric and then give the classification and asymptotic behavior of all radially symmetric gradient Yamabe solitons. We also show that any eternal solutions to the Yamabe flow with positive Ricci curvature and with the scalar curvature attaining an interior space-time maximum must be a steady Yamabe soliton.

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