Locally strongly convex affine hypersurfaces with parallel cubic form

Zejun Hu, Zhengzhou University Haizhong Li Tsinghua University Luc Vrancken Katholieke Universiteit Leuven

Differential Geometry mathscidoc:1609.10209

Journal of Differential Geometry, 87, (2), 239-307, 2011
We give a complete classification of locally strongly convex affine hypersurfaces of Rn+1 with parallel cubic form with respect to the Levi-Civita connection of the affine Berwald-Blaschke metric. It turns out that all such affine hypersurfaces are quadrics or can be obtained by applying repeatedly the Calabi product construction of hyperbolic affine hyperspheres, using as building blocks either the hyperboloid, or the standard immersion of one of the symmetric spaces SL(m,R)/SO(m), SL(m,C)/SU(m), SU 2m /Sp(m), or E6(−26)/F4.
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@inproceedings{zejun2011locally,
  title={LOCALLY STRONGLY CONVEX AFFINE HYPERSURFACES WITH PARALLEL CUBIC FORM},
  author={Zejun Hu,, Haizhong Li, and Luc Vrancken},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911231419468156866},
  booktitle={Journal of Differential Geometry},
  volume={87},
  number={2},
  pages={239-307},
  year={2011},
}
Zejun Hu,, Haizhong Li, and Luc Vrancken. LOCALLY STRONGLY CONVEX AFFINE HYPERSURFACES WITH PARALLEL CUBIC FORM. 2011. Vol. 87. In Journal of Differential Geometry. pp.239-307. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911231419468156866.
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