On hypersurfaces satisfying conditions determined by the Opozda-Verstraelen affine curvature tensor

摘要

Using the Blaschke-Berwald metric and the affine shape operator of a hypersurface M in the (n + 1)-dimensional real affine space we define a generalized curvature tensor called the Opozda-Verstraelen affine curvature tensor. We establish some pseudosymmetry type curvature conditions satisfied by this tensor for locally strongly convex hypersurfaces M, n > 2, with two distinct affine principal curvatures or with three distinct affine principal curvatures, assuming that at least one affine principal curvature is of multiplicity 1.