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Parallel surfaces in affine 4- space

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Abstract

We study affine immersions as introduced by Nomizu and Pinkall. We classify those affine immersions of a surface in R4 which are degenerate and have vanishing cubic form (i.e. parallel second fundamental form). This completes the classification of parallel surfaces of which the first results were obtained in the beginning of this century by Blaschke and his collaborators.

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Authors and Affiliations

  1. Technische Universitaet Berlin, Fakultaet II, Inst. f. Mathematik, MA 8-3, 10623, Berlin, Germany

    C. Scharlach

  2. LAMATH, Université de Valenciennes, ISTV2, 59313, Valenciennes, Cedex 9, France

    L. Vrancken

Authors
  1. C. Scharlach
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  2. L. Vrancken
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Correspondence to C. Scharlach or L. Vrancken.

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Scharlach, C., Vrancken, L. Parallel surfaces in affine 4- space. Abh.Math.Semin.Univ.Hambg. 73, 167–179 (2003). https://doi.org/10.1007/BF02941274

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  • DOI: https://doi.org/10.1007/BF02941274

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