Torsion of $\alpha$-connections on the density manifold

Nihat Ay; Lorenz J. Schwachhöfer

Torsion of $\alpha$-connections on the density manifold

Information Theory 2025-04-01 v1 math.IT

Authors: Nihat Ay , Lorenz J. Schwachhöfer

Abstract

We study the torsion of the $\alpha$ -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 $\alpha$ -connections are torsion free. For the $\alpha$ -connections obtained by the Otto metric, we show that, except for $\alpha = -1$ , they are not torsion free.

Keywords

density manifold $\alpha$-connections torsion Fisher-Rao metric Otto metric

Cite

@article{arxiv.2503.23588,
  title  = {Torsion of $\alpha$-connections on the density manifold},
  author = {Nihat Ay and Lorenz J. Schwachhöfer},
  journal= {arXiv preprint arXiv:2503.23588},
  year   = {2025}
}

Comments

8 pages

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