manuscripta mathematica

, Volume 108, Issue 2, pp 171–189 | Cite as

Harmonic maps in unfashionable geometries

  • Francis Burstall
  • Udo Hertrich-Jeromin


 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.


Differential Geometry General Construction Real Smooth Projective Differential Geometry 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Francis Burstall
    • 1
  • Udo Hertrich-Jeromin
    • 2
  1. 1.Department of Mathematics, University of Bath, Bath BA2 7AY, UK. e-mail:
  2. 2.Department of Mathematics, TU Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany. e-mail: udo@sfb288.math.tu-berlin.deDE

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