Singularities and Bifurcations of Pseudospherical Surfaces

David Brander, Farid Tari

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Abstract

We study singularities and bifurcations of constant negative curvature surfaces in Euclidean 3-space via their association with Lorentzian harmonic maps. This preprint presents the basic results on this, the full proofs of which will appear in an article under preparation. We show that the generic bifurcations in 1-parameter families of such surfaces are the Cuspidal Butterfly, Cuspidal Lips, Cuspidal Beaks, 2/5 Cuspidal edge and Shcherbak bifurcations
Original languageEnglish
JournalOberwolfach Preprints
Volume2020
Issue number08
Number of pages7
ISSN1864-7596
DOIs
Publication statusPublished - 2020

Keywords

  • Bifurcations
  • Constant Gauss curvature
  • Cauchy problem
  • Differential geometry
  • Discriminants
  • Frontals
  • Integrable systems
  • Loop groups
  • Pseudospherical surfaces
  • Singularities
  • Wave fronts
  • Wave maps

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