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On locally strongly convex affine hypersurfaces with parallel cubic form. Part I |
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| Authors: | Zejun Hu Haizhong Li Udo Simon Luc Vrancken |
| Institution: | a Department of Mathematics, Zhengzhou University, Zhengzhou 450052, People's Republic of China b Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China c Institut für Mathematik, MA 8-3, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany d LAMATH, ISTV2, Campus du mont houy, Université de Valenciennes, France |
| Abstract: | In this paper, we study locally strongly convex affine hypersurfaces of Rn+1 that have parallel cubic form with respect to the Levi-Civita connection of the affine Berwald-Blaschke metric; it is known that they are affine spheres. In dimension n?7 we give a complete classification of such hypersurfaces; in particular, we present new examples of affine spheres. |
| Keywords: | primary 53A15 secondary 53B25 |
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