Pavel Osipov: Statistical Lie algebras of constant curvature and locally conformally Kähler Lie algebras, 341-358

Abstract:

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 $TM\times{\mathbb{R}}$ by a statistical manifold of constant non-zero curvature on $M$. 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.

2010 Mathematics Subject Classification: 53C15.

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