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Locally strongly convex affine hypersurfaces with parallel cubic form
We give a complete classification of locally strongly convex affine hypersurfaces of R n+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 …