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<p>In this article, we give examples of rotational symmetric not totally umbilic Willmore immersions of a connected surface with countably many umbilic circles. Further we prove that any rotational symmetric Willmore immersion of a connected surface in codimension one with an umbilic line is after applying an appropriate Möbius transformation, which keeps the rotational symmetry, minimal in hyperbolic space outside its umbilic lines. As a consequence such immersions are isothermic.</p>

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Rotational symmetric Willmore surfaces with umbilic lines

  • 期刊论文

  • 发表日期：

    2025年8月10日

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  • Anna Dall’Acqua,
  • Reiner M. Schätzle

摘要

In this article, we give examples of rotational symmetric not totally umbilic Willmore immersions of a connected surface with countably many umbilic circles. Further we prove that any rotational symmetric Willmore immersion of a connected surface in codimension one with an umbilic line is after applying an appropriate Möbius transformation, which keeps the rotational symmetry, minimal in hyperbolic space outside its umbilic lines. As a consequence such immersions are isothermic.