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Harmonic maps in unfashionable geometries

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Abstract

 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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Authors and Affiliations

  1. Department of Mathematics, University of Bath, Bath BA2 7AY, UK. e-mail: feb@maths.bath.ac.uk, , , , , , GB

    Francis Burstall

  2. Department of Mathematics, TU Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany. e-mail: udo@sfb288.math.tu-berlin.de, , , , , , DE

    Udo Hertrich-Jeromin

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  1. Francis Burstall
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  2. Udo Hertrich-Jeromin
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Received: 3 August 2001

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Burstall, F., Hertrich-Jeromin, U. Harmonic maps in unfashionable geometries. Manuscripta Math. 108, 171–189 (2002). https://doi.org/10.1007/s002290200269

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  • DOI: https://doi.org/10.1007/s002290200269

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