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).
Results in Mathematics – Springer Journals
Published: Feb 8, 2017
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