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Quasi-Statistical Schouten–van Kampen Connections on the Tangent Bundle

Author

Listed:
  • Simona-Luiza Druta-Romaniuc

    (Department of Mathematics and Informatics, “Gheorghe Asachi” Technical University of Iaşi, Strada Dimitrie Mangeron, nr. 67A, 700050 Iaşi, Romania)

Abstract

We determine the general natural metrics G on the total space T M of the tangent bundle of a Riemannian manifold ( M , g ) such that the Schouten–van Kampen connection ∇ ¯ associated to the Levi-Civita connection of G is (quasi-)statistical. We prove that the base manifold must be a space form and in particular, when G is a natural diagonal metric, ( M , g ) must be locally flat. We prove that there exist one family of natural diagonal metrics and two families of proper general natural metrics such that ( T M , ∇ ¯ , G ) is a statistical manifold and one family of proper general natural metrics such that ( T M ∖ { 0 } , ∇ ¯ , G ) is a quasi-statistical manifold.

Suggested Citation

  • Simona-Luiza Druta-Romaniuc, 2023. "Quasi-Statistical Schouten–van Kampen Connections on the Tangent Bundle," Mathematics, MDPI, vol. 11(22), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4614-:d:1278041
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    References listed on IDEAS

    as
    1. Adela Mihai & Ion Mihai, 2018. "Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature," Mathematics, MDPI, vol. 6(3), pages 1-8, March.
    2. Yanlin Li & Manish Kumar Gupta & Suman Sharma & Sudhakar Kumar Chaubey, 2023. "On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space," Mathematics, MDPI, vol. 11(15), pages 1-13, August.
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