  We show that a statistical manifold manifold of a constant non-zero curvature
can be realised as a level line of Hessian potential on a Hessian cone. We
construct a Sasakian structure on $TM\times\R$ by a statistical manifold
manifold of a constant non-zero curvature on $M$. By a statistical Lie algebra
of a constant non-zero Lie algebra we construct a l.c.K Lie algebra.
