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Affine Differential Geometric Control Tools for Statistical Manifolds

Author

Listed:
  • Iulia-Elena Hirica

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
    These authors contributed equally to this work.)

  • Cristina-Liliana Pripoae

    (Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana 6, RO-010374 Bucharest, Romania
    These authors contributed equally to this work.)

  • Gabriel-Teodor Pripoae

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
    These authors contributed equally to this work.)

  • Vasile Preda

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

The paper generalizes and extends the notions of dual connections and of statistical manifold, with and without torsion. Links with the deformation algebras and with the Riemannian Rinehart algebras are established. The semi-Riemannian manifolds admitting flat dual connections with torsion are characterized, thus solving a problem suggested in 2000 by S. Amari and H. Nagaoka. New examples of statistical manifolds are constructed, within and beyond the classical setting. The invariant statistical structures on Lie groups are characterized and the dimension of their set is determined. Examples for the new defined geometrical objects are found in the theory of Information Geometry.

Suggested Citation

  • Iulia-Elena Hirica & Cristina-Liliana Pripoae & Gabriel-Teodor Pripoae & Vasile Preda, 2021. "Affine Differential Geometric Control Tools for Statistical Manifolds," Mathematics, MDPI, vol. 9(14), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1654-:d:593943
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    Citations

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    Cited by:

    1. Iulia-Elena Hirica & Cristina-Liliana Pripoae & Gabriel-Teodor Pripoae & Vasile Preda, 2022. "Conformal Control Tools for Statistical Manifolds and for γ -Manifolds," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    2. Cristina-Liliana Pripoae & Iulia-Elena Hirica & Gabriel-Teodor Pripoae & Vasile Preda, 2023. "Holonomic and Non-Holonomic Geometric Models Associated to the Gibbs–Helmholtz Equation," Mathematics, MDPI, vol. 11(18), pages 1-20, September.

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