The magid-ryan conjecture for equiaffine hyperspheres with constant sectional curvature

Journal of Differential Geometry

Volumn 54, Issue 1, 2000, Pages 99-138

  Vrancken, Luc ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Affine differential geometry; Affine hyperspheres; Constant sectional curvature

Indexed keywords

EID: 0002639555     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214342148     Document Type: Article

References (14)

1. E. Bergen, E. Ramakers & L. Vrancken, The magid-ryan conjecture for 4-dimensional affine spheres, Abh. Math. Sem. Univ. Hamburg 69 (1999) 139-157.
2. F. Dillen, M. Magid & L. Vrancken, Affine hyperspheres with constant affine sectional curvature, Geometry and Topology of Submanifolds X, (W.H. Chen et al. eds.), World Scientific Publising Co., 2000, 31-53.
3. F. Dillen, A. Martinez, F. Milan, F.G. Santos & L. Vrancken, On the Pick invariant, the affine mean curvature and the Gauss curvature of affine surfaces, Results Math. 20 (1991) 622-642.
4. [41 F. Dillen & L. Vrancken, Calabi type composition of affine spheres, Differential Geom. Appl. 4 (1994) 303-328.
5. J. A. Eidswick, A proof of newton’s power sum formulas, Amer. Math. Monthly 75 (1968) 396-397.
6. N. Ejiri, Totally real minimal immersions of n-dimensional real space forms into n-dimensional complex space forms, Proc. Amer. Math. Soc. 84 (1982) 243-246.
7. M. Kriele & L. Vrancken, Lorentzian affine hyperspheres with constant sectional curvature, Trans. Amer. Math. Soc. 352 (2000) 1581-1599.
8. A. M. Li, L. Vrancken & U. Simon, Affine spheres with constant affine sectional curvature, Math. Z. 206 (1991) 651-658.
9. A. M. Li, U. Simon & G. Zhao, Global affine differential geometry of hypersurfaces, Vol. 11 De Gruyter Expositions in Math., Walter De Gruyter, Berlin-New York, 1993.
10. M. Magid & P. Ryan, Affine 3-spheres with constant affine curvature, Trans. Amer. Math. Soc. 330 (1992) 887-901.
11. K. Nomizu & T. Sasaki, Affine differential geometry, Cambridge University Press, Cambridge, 1994.
12. J. Radon, Zur affingeometrie der regelflachen, Leipziger Berichte 70 (1918) 147-155.
13. U. Simon, Local classification of twodimensional affine spheres with constant curvature metric, Differential Geom. Appl. 1 (1991) 123-132.
14. L. Vrancken, Affine quasi umbilical hypersurfaces which a, re flat with respect to the affine metric, Results Math. 20 (1991) 756-776.