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

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

Mathematics, 2023, vol. 11, issue 22, 1-20

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.

Keywords: (pseudo-)Riemannian manifold; Codazzi pair; statistical manifold; quasi-statistical manifold; Schouten–van Kampen connection; tangent bundle; general natural metric (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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