Singularities and Bifurcations of Pseudospherical Surfaces

David Brander, Farid Tari

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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
Issue number08
Number of pages7
Publication statusPublished - 2020


  • 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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