Families of spherical surfaces and harmonic maps

David Brander*, Farid Tari

*Corresponding author for this work

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Abstract

We study singularities of constant positive Gaussian curvature surfaces and determine the way they bifurcate in generic 1-parameter families of such surfaces. We construct the bifurcations explicitly using loop group methods. Constant Gaussian curvature surfaces correspond to harmonic maps, and we examine the relationship between the two types of maps and their singularities. Finally, we determine which finitely \mathcal {A}-determined map-germs from the plane to the plane can be represented by harmonic maps.
Original languageEnglish
JournalGeometriae Dedicata
Number of pages23
ISSN0046-5755
DOIs
Publication statusPublished - 2018

Keywords

  • Bifurcations 
  • Differential geometry 
  • Discriminants 
  • Integrable systems
  • Loop groups 
  • Parallels 
  • Spherical surfaces
  • Constant Gauss curvature 
  • Singularities 
  • Cauchy problem 
  • Wave fronts 

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