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

Name: Statistical Lie algebras of a constant curvature and locally conformally Kähler Lie algebras
Creator: Osipov, Pavel
Keywords: Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2021Embargo end date: 01 Jan 2021Publisher:arXiv

Authors: Osipov, Pavel;

doi: 10.48550/arxiv.2112.06686

arXiv: http://arxiv.org/abs/2112.06686

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

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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 $TM\times\R$ 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.

Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics

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