On four-dimensional Einstein affine hyperspheres
The authors classify the 4-dimensional locally strongly convex affine hyperspheres whose affine metrics are Einstein. They prove the following: Theorem. Let \(x: M^4\to \mathbb R^5\) be a locally strongly convex affine hypersphere with its affine metric being Einstein, then it is locally affine equivalent to the open part of either one of the hyperquadrics, or the hyperbolic affine hypersphere \(Q(1, 4): x^1x^2x^3x^4x^5 = 1\), where \((x^1, \dots, x^5)\) are the coordinates of \(\mathbb R^5\).
scientific article; zbMATH DE number 6668717