We show that a statistical manifold of constant non-zero curvature
can be realised as a level set of Hessian potential on a Hessian
cone. We construct a Sasakian structure on
by
a statistical manifold of constant non-zero curvature on . By a
statistical Lie algebra of constant non-zero Lie algebra we
construct a l.c.K. Lie algebra.
Key Words: Statistical manifolds, l.c.K. manifolds,
Hessian manifolds, geometric structures on Lie groups and algebras.