On hypersurfaces satisfying conditions determined by the Opozda–Verstraelen affine curvature tensor
Volume 126 / 2021
Annales Polonici Mathematici 126 (2021), 215-240
MSC: Primary 53A15, 53B20.
DOI: 10.4064/ap200715-6-5
Published online: 6 October 2021
Abstract
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 $M$, $n \gt 2$, with two distinct affine principal curvatures or with three distinct affine principal curvatures, assuming that at least one affine principal curvature is of multiplicity $1$.
