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Degenerate homogeneous affine surfaces in ℝ3

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Abstract

We study degenerate homogeneous affine surfaces in ℝ3. It is proved that such a surface is either an open part of a plane, a cylinder on an ellipse, parabola or hyperbola or of the surface given byxz − 1/2y 2=0.

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References

  1. Dillen, F. and Vrancken, L.: Parallel hypersurfaces in affine spaces, Preprint.

  2. Nomizu, K. and Sasaki, T.: A new model of unimodular-affinely homogeneous surface,Manuscripta Math. 73 (1991), 39–44.

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  3. Guggenheimer, H.:Differential Geometry, McGraw-Hill, New York, 1963.

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

    Luc Vrancken

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  1. Luc Vrancken
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Vrancken, L. Degenerate homogeneous affine surfaces in ℝ3 . Geom Dedicata 53, 333–351 (1994). https://doi.org/10.1007/BF01264006

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  • DOI: https://doi.org/10.1007/BF01264006

Mathematics Subject Classifications (1991)

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