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Indefinite Affine Umbilical Surfaces in \(R^4 \)

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Abstract

We study surfaces M 2 in the four-dimensional affine space \(R^4 \) equipped with its usual torsion-free connection D and parallel volume form given by the determinant.

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References

  1. Burstin, C. and Mayer, W.: Die Geometrie zweifach ausgedehnter Mannigfaltigkeiten F 2 im affinen Raum R 4, Math. Z. 26 (1927), 373–407.

    Google Scholar 

  2. Cecil, T., Magid, M. and Vrancken, L.: An affine characterization of the Veronese surface, Geom. Dedicata 57 (1995), 55–71.

    Google Scholar 

  3. Dillen, F., Mys, G., Verstraelen, L. and Vrancken, L.: The affine mean curvature vector for surfaces in R 4, Math. Nachr. 166 (1994), 155–165.

    Google Scholar 

  4. Li, J.: Harmonic surfaces in R 4, Preprint.

  5. Martinez, A. and Milan, F.: A characterization of the complex paraboloid, Results Math. 27 (1995), 302–307.

    Google Scholar 

  6. Magid, M., Scharlach, C. and Vrancken, L: Affine umbilical surfaces in R 4, Manuscripta Math. 88 (1995), 275–289.

    Google Scholar 

  7. Magid, M. and Vrancken, L.: Flat affine surfaces with flat normal connection, Geometriae Dedicata, to appear.

  8. Nomizu, K. and Vrancken, L.: A new equiaffine theory for surfaces in R 4, Internat. J. Math. 4 (1993), 127–165.

    Google Scholar 

  9. Vrancken, L.: Affine surfaces whose geodesics are planar curves, Proc. Amer. Math. Soc. 123 (1995), 3851–3854.

    Google Scholar 

  10. Vrancken, L.: Thomsen surfaces in affine 4–space, Monatsh. Math. 122 (1996), 251–264.

    Google Scholar 

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Authors and Affiliations

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

    L. Verstraelen

  2. Fachbereich Mathematik, Technische Universitäat Berlin, Sekr. MA 8-3, Strasse des 17. Juni 136, D-10623, Berlin, Germany

    L. Vrancken

  3. Katedra Matematyki, Politechniki Rzeszowskiej, ul.W.Pola 2, PL-35-959, Rzeszow, Poland

    P. Witowicz

Authors
  1. L. Verstraelen
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  2. L. Vrancken
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  3. P. Witowicz
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Verstraelen, L., Vrancken, L. & Witowicz, P. Indefinite Affine Umbilical Surfaces in \(R^4 \) . Geometriae Dedicata 79, 109–119 (2000). https://doi.org/10.1023/A:1005039604280

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  • DOI: https://doi.org/10.1023/A:1005039604280

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