Statistical Lie algebras of a constant curvature and locally conformally Kähler Lie algebras

2021/12/13 by Pavel Osipov, Osipov, Pavel
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2112.06686

openalex publication_date 2021/12/13 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28

Abstract

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×\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.

Related

• On a constant curvature statistical manifold
• Curvature bounded conjugate symmetric statistical structures with\n complete metric
• Locally conformally Hessian and statistical manifolds
• Immersions into Statistical Manifolds
• A sectional curvature for statistical structures