Abstract
We consider affine-complete Blaschke hypersurfaces with constant negative affine mean curvature; for a subclass we assume appropriate bounds for the affine shape operator and for the affine support function; we investigate whether in this subclass of hypersurfaces there exist examples that are not hyperbolic affine spheres. Examples of Calabi type compositions, given by Dillen and Vrancken, admit to test the assumptions of our Main Theorem on this subclass. The study of Blaschke hypersurfaces with negative affine mean curvature finally leads to investigations of the scalar curvature: we treat the scalar curvature of affine spheres in the last section.
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