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<p>In this paper we investigate gradient Yamabe solitons, either shrinking or steady, that can be isometrically immersed into space forms as hypersurfaces that admit an upper bound on the norm of their second fundamental form. Those solitons satisfying an additional condition, that could be constant mean curvature or the number of critical points of the potential function being at most one, are fully classified. Our argument is based on the weak Omori-Yau principle for the drifted Laplacian on Riemannian manifolds.</p>

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Classification of gradient Yamabe soliton hypersurfaces of space forms

  • 期刊论文

  • 发表日期：

    2025年5月12日

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  • Willian Isao Tokura,
  • Marcelo Bezerra Barboza

摘要

In this paper we investigate gradient Yamabe solitons, either shrinking or steady, that can be isometrically immersed into space forms as hypersurfaces that admit an upper bound on the norm of their second fundamental form. Those solitons satisfying an additional condition, that could be constant mean curvature or the number of critical points of the potential function being at most one, are fully classified. Our argument is based on the weak Omori-Yau principle for the drifted Laplacian on Riemannian manifolds.