manuscripta mathematica

, Volume 108, Issue 2, pp 171-189

First online:

Harmonic maps in unfashionable geometries

  • Francis BurstallAffiliated withDepartment of Mathematics, University of Bath, Bath BA2 7AY, UK. e-mail:
  • , Udo Hertrich-JerominAffiliated withDepartment of Mathematics, TU Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany. e-mail:

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 We describe some general constructions on a real smooth projective 4-quadric which provide analogues of the Willmore functional and conformal Gauss map in Lie sphere and projective differential geometry. Extrema of these functionals are characterized by harmonicity of this Gauss map.