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<p>An inequality between the Willmore and Weyl functionals on compact submanifolds immersed in a Riemannian warped product is obtained. Furthermore, we characterize when the equality occurs. In this case, either the submanifold is totally umbilical, or it has two distinct principal curvatures with the same multiplicity, being conformal to a Riemannian product of two manifolds.</p>

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On the Weyl and Willmore Functionals for Submanifolds in a Warped Product

  • 期刊论文

  • 发表日期：

    2025年11月18日

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  • Fábio R. dos Santos,
  • Thays I. dos Santos Nunes

摘要

An inequality between the Willmore and Weyl functionals on compact submanifolds immersed in a Riemannian warped product is obtained. Furthermore, we characterize when the equality occurs. In this case, either the submanifold is totally umbilical, or it has two distinct principal curvatures with the same multiplicity, being conformal to a Riemannian product of two manifolds.