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<p>We apply Singularity Theory techniques in order to provide geometrical characterizations of the different singularities of the Gauss map on 3-manifolds generically immersed in Euclidean 4-space. The Gauss map can be seen as the catastrophe map associated with the family of height function on the 3-manifold. We obtain different characterizations for such generic singularities in terms of the limit of certain sequences of points with specific geometrical properties, that is, sequences of points with bitangent and tritangent hyperplanes given by the family of height function.</p>

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Geometrical characterizations of singularities of the Gauss map on generically immersed 3-manifolds in \({\mathbb {R}}^4\)

  • 期刊论文

  • 发表日期：

    2025年2月25日

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  • Ana Claudia Nabarro,
  • Maria del Carmen Romero-Fuster,
  • Maria Carolina Zanardo

摘要

We apply Singularity Theory techniques in order to provide geometrical characterizations of the different singularities of the Gauss map on 3-manifolds generically immersed in Euclidean 4-space. The Gauss map can be seen as the catastrophe map associated with the family of height function on the 3-manifold. We obtain different characterizations for such generic singularities in terms of the limit of certain sequences of points with specific geometrical properties, that is, sequences of points with bitangent and tritangent hyperplanes given by the family of height function.