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Thomsen surfaces in affine 4-space

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Abstract

Surfaces which are both affine and Euclidean minimal are called Thomsen surfaces. In ℝ3, these surfaces have been completely classified byBarthel, Volkmer andHaubitz. A similar problem, in the Lorentzian 3-space was solved byMagid. In the present paper, we study Thomsen surfaces in ℝ4 and show that these surfaces are affine equivalent to the complex paraboloid.

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Authors and Affiliations

  1. Department Wiskunde, K. U. Leuven, Celestijnenlaan 200 B, B-3001, Leuven, Belgium

    Luc Vrancken

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  1. Luc Vrancken
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The author is a Senior Research Assistant of the National Fund, for Scientific Research (Belgium). This work was done while the author visited Brown University (Providence, USA) in April 93. He would like to thank Professors T. Cecil, M. Magid, and K. Nomizu for their hospitality.

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Vrancken, L. Thomsen surfaces in affine 4-space. Monatshefte für Mathematik 122, 251–264 (1996). https://doi.org/10.1007/BF01320188

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  • DOI: https://doi.org/10.1007/BF01320188

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