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Blaschke, W.: Vorlesungen über Differentialgeometrie. II. Affine Differentialgeometrie. Berlin Heidelberg New York: Springer 1923
Bokan, N., Nomizu, K., Simon, U.: Affine hypersurfaces with parallel cubic forms. Tôhoku Math. J., II. Ser.42, 101–108 (1990)
Calabi, E.: Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jögens. Mich. Math. J.5, 105–126 (1958)
Calabi, E.: Complete affine hypersurfaces. I. Symp. Math.10, 19–38 (1972)
Cheng, S.Y., Yau, S.T.: Complete affine hypersurfaces, part I, the completeness of affine metrics, Commun. Pure Appl. Math.36, 839–866 (1986)
Li, A.M.: Calabi conjecture on hyperbolic affine hyperspheres. Math. Z.203, 483–491 (1990)
Li, A.M.: Some theorems in affine differential geometry. Acta Math. Sin. New Ser.5 (no. 4), 345–354 (1989)
Li, A.M., Penn, G.: Uniqueness theorems in affine differential geometry, part II. Results Math.13, 308–317 (1988)
Magid, A., Ryan, P.: Flat affine spheres in ℝ3. Geom. Dedicata33 (no. 3), 277–288 (1990)
Magid, A., Ryan, P.: Affine 3-spheres with constant affine curvature. Trans. Am. Math. Soc. (to appear)
Nomizu, K.: Introduction to affine differential geometry, part I. Lecture Notes. Preprint 88-37. MPI (1988)
Nomizu, K.: A survey of recent results in affine differential geometry. In: Verstraelen, L., West, A. (eds.) Geometry and Topology of Submanifolds, III. Leeds-Conference 1990, pp. 227–256. Singapore: World Scientific 1991
Nomizu, K., Pinkall, U.: Cayley surfaces in affine differential geometry. Tôhoku Math. J., II. Ser.41 (no. 4), 589–596 (1989)
Radon, J.: Zur Affingeometrie der Regelflächen. Leip. Ber.70, 147–155 (1918)
Sasaki, T.: Hyperbolic affine hyperspheres. Nagoya Math. J.77, 107–123 (1980)
Schneider, R.: Zur affinen Differentialgeometrie im Großen. II. Über eine Abschätzung der Pickschen Invariante auf Affinesphären. Math. Z.102, 1–8 (1967)
Simon, U.: Local classification of two dimensional affine spheres with constant curvature metric. Differe. Geom. Appl.1, 123–132 (1991)
Simon, U.: Recent developments in affine differential geometry. In: Bokan, N. et al. (eds.) Proceedings of the Conference Differential Geometry and its Applications, 1988, pp. 327–347. Dubrovnik, Yugoslavie: Novi Sad 1989
Simon, U.: Zur Entwicklung der affinen Differentialgeometrie nach Blaschke. In: Buran, W. et al. (eds.) W. Blaschke, Gesammelte Werke. Essen: Bd. IV, pp. 35–88. Thales 1985
Simon, U., Wang, C.P.: Local theory of affine 2-spheres. In: Greene, R.E., Yau, S.T. (eds.) Proceedings 1990 Summer Institute of Differential Geometry. (to appear)
Vrancken, L., Li, A.M., Simon, U.: Affine spheres with constant sectional curvature. Math. Z.206, 651–658 (1991)
Wang, C.P.: Some examples of complete hyperbolic affine 2-spheres in ℝ3. In: Ferus, D. et al. (eds.) Proceedings Conf. Global Analysis Global Differential Geometry, Berlin 1990. (Lect. Notes Math., vol. 1481, pp. 272–280) Berlin Heidelberg New York: Springer 1991
Yu, J.H.: Affine spheres with constant sectional curvature inA 4. J. Sichuan Univ., Nat. Sci. Ed.27, no. 4 (1990)
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Wang, C. Canonical equiaffine hypersurfaces in ℝn+1 . Math Z 214, 579–592 (1993). https://doi.org/10.1007/BF02572426
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DOI: https://doi.org/10.1007/BF02572426