A flat affine manifold is a differentiable manifold equipped with a linear flat torsion-free connection. A Hessian manifold is a flat affine manifold with a Riemannian metric which is locally equivalent to the Hessian of a function. Equivalently, a Hessian manifold is a flat affine manifold \((M, \nabla)\) endowed with a Riemannian metric \(g\) such that the tensor \(\nabla g\) is totally symmetric. A statistical manifold \((M, D, g)\) is a manifold \(M\) endowed with a torsion-free connection \(D\) and a Riemannian metric \(g\) such that the tensor \(Dg\) is totally symmetric (for relation between information geometry and affine differential geometry see H. Matsuzoe [Adv. Stud. Pure Math. 57, 303–321 (2010; Zbl 1201.53011)]). A statistical manifold \((M, D, g)\) is said to be of constant curvature \(c\) if the curvature tensor \(\Theta_D\) satisfies \(\Theta_D (X, Y) Z = c (g(Y, Z) X - g(X, Z)Y)\). A Riemannian manifold \((M, g)\) is called Sasakian if there exists a complex structure \(I\) on the cone \((M \times R^{>0}, s^2 g_M + ds^2\) such that \((M \times R^{>0}, s^2 g_M + ds^2, I)\) is a Kähler manifold. (This definition of Sasakian manifolds is equivalent to the standard one, see C. P. Boyer and K. Galicki [Sasakian geometry. Oxford: Oxford University Press (2008; Zbl 1155.53002)]; D. V. Alekseevsky et al. [Int. J. Math. 26, No. 6, Article ID 1541001, 29 p. (2015; Zbl 1319.32017)]. In the paper under review the author shows that a statistical manifold of constant curvature can be realised as a level set of a Hessian potential on a Hessian cone, thus, as a Sasakian manifold is a level set of the Kähler potential of a Kähler cone, statistical manifolds of constant curvature are real analogue of Sasakian manifolds. He proves Theorem 1.1. “Let \((M, g, \nabla)\) be a statistical manifold of constant curvature. Then \(T M \times R\) admits a structure of a Sasakian manifold”. Then the author considers Lie groups and Lie algebras with the corresponding invariant geometrical structures. In particular, by a statistical Lie algebra of constant non-zero curvature he constructs a locally conformally Kähler Lie algebra”.