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08 February 2025
 
  » arxiv » 1109.0243

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A note on the global structure of conformal gradient solitons with nonnegative Ricci tensor
Giovanni Catino ; Carlo Mantegazza ; Lorenzo Mazzieri ;
Date 1 Sep 2011
AbstractIn this note we will prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product $RR imes N^{n-1}$, or globally conformally equivalent to the Euclidean space $RR^{n}$ or to the round sphere $SS^{n}$. In particular, we will show that any complete, noncompact, gradient Yamabe--type soliton with positive Ricci tensor is rotationally symmetric, whenever the potential function is nonconstant.
Source arXiv, 1109.0243
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