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The fundamental theorem in affine hypersurface theory

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References

  1. Barthel, W. and Volkmer, R., ‘Die Bedeutung Christoffelscher Zusammenhänge in der affinen Differentialgeometrie’, E. B. Christoffel-Symp. Aachen, 1979, (1981), 568–589 [Zbl. 482.53007].

  2. Blaschke, W., ‘Vorlesungen über Differentialgeometrie II’, Affine Differentialgeometrie, Springer, Berlin, 1923.

    Google Scholar 

  3. Calabi, E., ‘Géométrie différentielle affine des hypersurfaces’, Sém. Bourbaki; 33e année, Vol. 1980/81, Exp. 573, Lect. Notes Math. 901 (1981), 189–204 [Zbl. 475.53021].

  4. Calabi, E., ‘Hypersurfaces with Maximal Affinely Invariant Area’, Amer. J. Math. 104 (1982), 91–126.

    Google Scholar 

  5. Eisenhart, L. P. Riemannian Geometry, Princeton Univ. Press, Sec. print, 1949.

  6. Laugwitz, D., Differentialgeometrie in Vektorräumen, Vieweg Braunschweig, 1965.

  7. Münzner, H. -F., ‘Die Poincarésche Indexmethode und ihre Anwendungen in der affinen Flächentheorie im Großen’, Dissertation, FU Berlin, 1963.

    Google Scholar 

  8. Oliker, V. and Simon, U., ‘The Christoffel Problem in Relative Differential Geometry’, Manuscript, TU Berlin, Emory Univ., Atlanta, 1984.

    Google Scholar 

  9. Schirokow, P. A. and Schirokow, A. P., Affine Differentialgeometrie, Teubner, Leipzig, 1962 [Zbl. 106.147; Russ. Original Zbl. 85.367].

    Google Scholar 

  10. Schneider, R. ‘Zur affinen Differentialgeometrie im Großen I’, Math. Z. 101 (1967), 375–406.

    Google Scholar 

  11. Schouten, J. A., Ricci-Calculus, (2nd edn), Springer, Berlin, Heidelberg, New York, 1954.

    Google Scholar 

  12. Simon, U., ‘Minkowskische Integralformeln und ihre Anwendungen in der Differentialgeometrie im Großen’, Math. Annalen 173 (1967), 307–321.

    Google Scholar 

  13. Simon, U., ‘Zur Relativgeometrie: Symmetrische Zusammenhänge auf Hyperflächen’, Math. Z. 106 (1968), 36–46.

    Google Scholar 

  14. Simon, U., ‘Kongruenzsätze der affinen Differentialgeometrien’, Math. Z. 120 (1971), 365–368.

    Google Scholar 

  15. Simon, U., ‘Die Entwicklung der affinen Differentialgeometrie nach Blaschke’, Kommentar in W.Blaschke, Gesammelte Werke, Bd. 4, Thales Verlag, Essen (1985), 35–88.

    Google Scholar 

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Simon, U. The fundamental theorem in affine hypersurface theory. Geom Dedicata 26, 125–137 (1988). https://doi.org/10.1007/BF00151665

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