The Journal of Geometric Analysis

, Volume 28, Issue 4, pp 3708–3717 | Cite as

Metrically Un-knotted Corank 1 Singularities of Surfaces in \(\mathbb {R}^4\)

  • L. BirbrairEmail author
  • Rodrigo Mendes
  • J. J. Nuño-Ballesteros


The paper is devoted to relations between topological and metric properties of germs of real surfaces, obtained by analytic maps from \(\mathbb {R}^2\) to \(\mathbb {R}^4.\) We show that for a big class of such surfaces, the normal embedding property implies the triviality of the knot, presenting the link of the surfaces. We also present some criteria of normal embedding in terms of the polar curves.


Normal embedding Link Isolated singularity 

Mathematics Subject Classification

14B05 32S50 58K15 



We would like to thank Alexandre Fernandes, Vincent Grandjean, and Edson Sampaio for interesting discussions and important remarks.


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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  • L. Birbrair
    • 1
    Email author
  • Rodrigo Mendes
    • 2
  • J. J. Nuño-Ballesteros
    • 3
  1. 1.Departamento of MatemáticaUniversidade Federal do CearáFortalezaBrazil
  2. 2.Instituto de Ciências Exatas e da NaturezaUniversidade de Integração Internacional da Lusofonia Afro-Brasileira (Unilab)AcarapeBrazil
  3. 3.Departament de MatemàtiquesUniversitat de ValènciaBurjassotSpain

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