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Classification of the Locally Strongly Convex Centroaffine Hypersurfaces with Parallel Cubic Form

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Abstract

In this paper, we study locally strongly convex centroaffine hypersurfaces with parallel cubic form with respect to the Levi–Civita connection of the centroaffine metric. As the main result, we obtain a complete classification of such centroaffine hypersurfaces. The result of this paper is a centroaffine version of the complete classification of locally strongly convex equiaffine hypersurfaces with parallel cubic form due to Hu et al. (J Differ Geom 87:239–307, 2011).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, People’s Republic of China

    Xiuxiu Cheng & Zejun Hu

  2. LAMAV, ISTV 2, Université de Valenciennes Et du Hainaut-Cambrésis, 59300, Valenciennes, France

    Marilena Moruz

Authors
  1. Xiuxiu Cheng
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  2. Zejun Hu
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  3. Marilena Moruz
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Corresponding author

Correspondence to Zejun Hu.

Additional information

This project was supported by NSFC (Grant No. 11371330).

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Cheng, X., Hu, Z. & Moruz, M. Classification of the Locally Strongly Convex Centroaffine Hypersurfaces with Parallel Cubic Form. Results Math 72, 419–469 (2017). https://doi.org/10.1007/s00025-017-0651-2

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  • DOI: https://doi.org/10.1007/s00025-017-0651-2

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