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Affine surfaces with constant affine curvatures

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Abstract

In this paper, we study affine non-degenerate Blaschke immersions from a surface M in ℝ3. We will assume that M has constant affine curvature and constant affine mean curvature, i.e. both the determinant and the trace of the shape operator are constant. Clearly, affine spheres satisfy both these conditions. In this paper, we completely classify the affine surfaces with constant affine curvature and constant affine mean curvature, which are not affine spheres.

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References

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Authors and Affiliations

  1. Faculteit Wetenschappen, Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3030, Leuven, Belgium

    Luc Vrancken

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  1. Luc Vrancken
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Research Assistant of the National Fund for Scientific Research (Belgium).

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Vrancken, L. Affine surfaces with constant affine curvatures. Geom Dedicata 33, 177–194 (1990). https://doi.org/10.1007/BF00183083

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  • DOI: https://doi.org/10.1007/BF00183083

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