Locally homogeneous affine hyperspheres with constant sectional curvature

Abstract

In this paper, we study the n-dimensional locally homogeneous affine hyperspheres with constant sectional curvature, vanishing Pick invariant and the difference tensor K satisfying Kⁿ⁻¹ ≠ 0. As main results, we classify such hyperspheres for dimension n ≤ 5.