Differential geometry and its applications vol:4 issue:4 pages:303-328
We give several ways of constructing new nondegenerate affine hypersurfaces in R(n+1) starting from some given proper or improper affine spheres. The resulting hypersurfaces can be forced to have nice properties, if the original affine spheres are chosen appropriately. In this way we obtain new examples of nondegenerate locally homogeneous affine hypersurfaces and of proper and improper affine spheres. We also discuss the properties of the affine metric of the hypersurface, such as the curvature or completeness. Finally we discuss the relation with projective transformations.