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Affine Quasi Umbilical Hypersurfaces which are flat with Respect to the Affine Metric

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References

  1. W. Blaschke, Vorlesungen über Differentialgeometrie II, Affine Differentialgeometrie, Springer, Berlin, 1968.

  2. F. Dillen, K. Nomizu and L. Vrancken, Monatshefte für Mathematik 109 (1990), 221–235.

    Article  MathSciNet  MATH  Google Scholar 

  3. A.M. Li, Some theorems in affine differential geometry, Acta Math. Sinica, N. S. 5 (1989), 345–354.

    Article  MathSciNet  MATH  Google Scholar 

  4. A.M. Li and G. Penn, Uniqueness theorems in affine differential geometry II, Results in Math. 13 (1988), 308–317.

    MathSciNet  MATH  Google Scholar 

  5. M. Magid and P. Ryan, Flat affine spheres, Geom. Dedicata 33 (1990), 277–288.

    Article  MathSciNet  MATH  Google Scholar 

  6. K. Nomizu, Introduction to affine differential geometry, part I, MPI/88-37, Bonn (1988).

  7. K. Nomizu and U. Pinkall, On the geometry of affine immersions, Math. Z. 195 (1987), 165–178.

    Article  MathSciNet  MATH  Google Scholar 

  8. U. Pinkall -, Cubic form theorem for affine immersions, Results in Math. 13 (1988), 338–362.

    MathSciNet  MATH  Google Scholar 

  9. J. Radon, Zur Affingeometrie der Regelflächen, Leipziger Berichte 70 (1918), 147–155.

    Google Scholar 

  10. U. Simon, Local classification of twodimensional affine spheres with constant curvature metric, Diff. Geom. and Applications, vol. 1, 1991, pp. 123–132.

    Article  MATH  Google Scholar 

  11. Z.I. Szabó, Structure theorems on Riemannian spaces satisfying R(X, Y).R = 0, I. The local version, J. DifF. Geom. 17 (1982), 531–582.

    MATH  Google Scholar 

  12. L. Vrancken, A. M. Li and U. Simon, Affine spheres with constant affine sectional curvature, Math. Z. 206 (1991), 651–658.

    Article  MathSciNet  MATH  Google Scholar 

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Vrancken, L. Affine Quasi Umbilical Hypersurfaces which are flat with Respect to the Affine Metric. Results. Math. 20, 756–776 (1991). https://doi.org/10.1007/BF03323209

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