manuscripta mathematica

, Volume 108, Issue 2, pp 171–189

Harmonic maps in unfashionable geometries


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

DOI: 10.1007/s002290200269

Cite this article as:
Burstall, F. & Hertrich-Jeromin, U. Manuscripta Math. (2002) 108: 171. doi:10.1007/s002290200269


 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.

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© Springer-Verlag Berlin Heidelberg 2002