Isotropic affine spheres

In this paper, we study affine spheres which are isotropic and we obtain a complete classification. In particular, we show that all such affine spheres are hyperbolic affine spheres, isometric with SL(3,ℝ)/SO(3), SL(3,ℂ)/SU(3), SU*(6)/Sp(3) or E 6(−26)/F 4.