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Conformal Control Tools for Statistical Manifolds and for γ -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
    “Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of Romanian Academy, 2. Calea 13 Septembrie, nr.13, Sect. 5, RO-050711 Bucharest, Romania
    “Costin C. Kiritescu” National Institute of Economic Research of Romanian Academy, 3. Calea 13 Septembrie, nr.13, Sect. 5, RO-050711 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

The theory of statistical manifolds w.r.t. a conformal structure is reviewed in a creative manner and developed. By analogy, the γ -manifolds are introduced. New conformal invariant tools are defined. A necessary condition for the f -conformal equivalence of γ -manifolds is found, extending that for the α -conformal equivalence for statistical manifolds. Certain examples of these new defined geometrical objects are given in the theory of Iinformation.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1061-:d:779814
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    References listed on IDEAS

    as
    1. 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.
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    Cited by:

    1. 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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    1. 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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