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<p>In this article, we study geometric and analytical features of complete expanding gradient weighted Yamabe solitons, which are self-similar solutions of the weighted Yamabe flow. We show that if the weighted scalar curvature is greater than the soliton constant by an arbitrarily small positive constant, then the soliton is trivial. In contrast, if the weighted scalar curvature is less than the soliton constant by an arbitrarily small positive constant, then the soliton is rotationally symmetric. In addition, we completely classify nontrivial complete expanding gradient weighted Yamabe soliton under some assumed conditions.</p>

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Classification of Complete Expanding Gradient Weighted Yamabe Solitons

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月5日

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  • Rong Mi

摘要

In this article, we study geometric and analytical features of complete expanding gradient weighted Yamabe solitons, which are self-similar solutions of the weighted Yamabe flow. We show that if the weighted scalar curvature is greater than the soliton constant by an arbitrarily small positive constant, then the soliton is trivial. In contrast, if the weighted scalar curvature is less than the soliton constant by an arbitrarily small positive constant, then the soliton is rotationally symmetric. In addition, we completely classify nontrivial complete expanding gradient weighted Yamabe soliton under some assumed conditions.