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- Title
Quasi-Statistical Schouten–van Kampen Connections on the Tangent Bundle.
- Authors
Druta-Romaniuc, Simona-Luiza
- 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.
- Subjects
TANGENT bundles; RIEMANNIAN manifolds; RIEMANNIAN metric
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 22, p4614
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11224614