Torsion of α-connections on the density manifold

2025/03/30 by Ay, Nihat, Schwachhöfer, Lorenz J.
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2503.23588

Abstract

We study the torsion of the α-connections defined on the density manifold in terms of a regular Riemannian metric. In the case of the Fisher-Rao metric our results confirm the fact that all α-connections are torsion free. For the α-connections obtained by the Otto metric, we show that, except for α= -1, they are not torsion free.

Related

• On a Torsion/Curvature Analogue of Dual Connections and Statistical Manifolds
• Torsion-free Connections with prescribed Curvature
• On two notions of torsion and metric compatibility of connections in noncommutative geometry
• Lorentzian connections with parallel twistor-free torsion
• Canonical Torsion-Free Connections on the Total Space of the Tangent and the Cotangent Bundle