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<p>In this paper, we study complete, nontrivial quasi-Yamabe gradient solitons and obtain partial classification results under natural scalar curvature bounds. Assuming that the scalar curvature is bounded from below or above by the soliton constant, we reduce the problem to a one-dimensional ordinary differential equation and derive several rigidity results. For shrinking and steady solitons with scalar curvature strictly larger than the soliton constant and a positive coefficient of the gradient term, we prove rotational symmetry, whereas for expanding and steady solitons with scalar curvature strictly smaller than the soliton constant and a negative coefficient, we obtain explicit warped-product models whose behavior at infinity is completely determined.</p>

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Complete quasi-Yamabe gradient solitons with bounded scalar curvature

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Shun Maeta

摘要

In this paper, we study complete, nontrivial quasi-Yamabe gradient solitons and obtain partial classification results under natural scalar curvature bounds. Assuming that the scalar curvature is bounded from below or above by the soliton constant, we reduce the problem to a one-dimensional ordinary differential equation and derive several rigidity results. For shrinking and steady solitons with scalar curvature strictly larger than the soliton constant and a positive coefficient of the gradient term, we prove rotational symmetry, whereas for expanding and steady solitons with scalar curvature strictly smaller than the soliton constant and a negative coefficient, we obtain explicit warped-product models whose behavior at infinity is completely determined.