An extremal class of three-dimensional hyperbolic affine spheres (Q1125231)

The paper is a contribution to the classification of affine spheres. The authors classify three-dimensional hyperbolic affine spheres which extremize a curvature invariant, analogous to one introduced by \textit{B.-Y. Chen} [Arch. Math. 60, 568-578 (1993; Zbl 0811.53060)] [see also \textit{C. Scharlach}, \textit{U. Simon}, \textit{L. Verstraden} and \textit{L. Vrancken}, Beitr. Algebra Geom. 38, 437-458 (1997; Zbl 0884.53013)]. The corresponding characterization in the case of elliptic affine spheres is due to the authors and \textit{C. Scharlach} [``An extremal class of 3-dimensional elliptic affine spheres'', to appear in Hokkaido Math. J.].