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1 results

  • 1 - A Bundle Approach to Conformal Surfaces in Space-Forms

  • Áurea Casinhas Quintino, Universidade Nova de Lisboa, Portugal
  • Book:
    Constrained Willmore Surfaces
    Published online:
    13 May 2021
    Print publication:
    10 June 2021, pp 16-30

  • Summary

    Our study is one of the geometrical aspects that are invariant under Möbius transformations. We present a Möbius description of space-forms in the projectivized light-cone. Such description is based on Darboux's model of the conformal n-sphere on the projective space of the light-cone in (n+1,1)-space, which, in particular, yields a conformal description of Euclidean n-spaces and hyperbolic n-spaces as submanifolds of the projectivized light-cone. With this, we approach a surface conformally immersed in a space-form as a null line subbundle of the Lorentzian trivial bundle over the surface.