Lorentzian affine hyperspheres with constant affine sectional curvature

We study ane hyperspheres M with constant sectional curvature (with respect to the ane metric h). A conjecture by M. Magid and P. Ryan states that every such ane hypersphere with nonzero Pick invariant is anely equivalent to either where the dimension n satises n =2 m 1o rn =2 m .U p to now, this conjecture was proved if M is positive denite or if M is a 3-dimensional Lorentz space. In this paper, we give an armative answer to this conjecture for arbitrary dimensional Lorentzian ane hyperspheres.