Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric
| Autor: | Esa Sharahi, Vladimir Balan, Esmaeil Peyghan |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Tangent bundle
Matematik Pure mathematics Holomorphic function Structure (category theory) General Medicine Base (topology) Statistical structure Statistical manifold Sasaki metric Holomorphic statistical manifold statistical structure Kähler structure Sasaki metric Mathematics::Differential Geometry Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Volume: 49, Issue: 1 120-135 Hacettepe Journal of Mathematics and Statistics |
| ISSN: | 1303-5010 2651-477X |
| DOI: | 10.15672/hjms.2019.667 |
| Popis: | The first part of the paper is devoted to the classification of the statistical structures which live on the tangent bundle of a statistical manifold endowed with a Sasaki metric. Further, considering a Kahler structure on the base statistical manifold, we introduce a family of almost complex structures on the tangent bundle equipped with the Sasaki metric, and find equivalent conditions for which this family induces a Kahler structure. Finally, we derive equivalent conditions for existence of holomorphic structures on the tangent bundle equipped with the Sasaki metric in the presence of a statistical structure. Several illustrative examples are provided, as well. |
| Databáze: | OpenAIRE |
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