Abstract
In this paper, we study locally strongly convex centroaffine hypersurfaces with vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of centroaffine metric. As the main result, we classify such hypersurfaces being not of flat centroaffine metric. In particular, 2,3-dimensional locally strongly convex centroaffine hypersurfaces with semi-parallel cubic form are completely determined.
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