Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical Submersions
In this paper we investigate statistical manifolds with almost quaternionic structures. We define the concept of quaternionic Kähler-like statistical manifold and derive the main properties of quaternionic Kähler-like statistical submersions, extending in a new setting some previous results obtained...
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-09-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/17/9/6213 |
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| author | Alina-Daniela Vîlcu Gabriel-Eduard Vîlcu |
| author_facet | Alina-Daniela Vîlcu Gabriel-Eduard Vîlcu |
| author_sort | Alina-Daniela Vîlcu |
| collection | DOAJ |
| description | In this paper we investigate statistical manifolds with almost quaternionic structures. We define the concept of quaternionic Kähler-like statistical manifold and derive the main properties of quaternionic Kähler-like statistical submersions, extending in a new setting some previous results obtained by K. Takano concerning statistical manifolds endowed with almost complex and almost contact structures. Finally, we give a nontrivial example and propose some open problems in the field for further research. |
| first_indexed | 2024-04-11T13:03:04Z |
| format | Article |
| id | doaj.art-be87475b14094c5995530e5f7727914d |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T13:03:04Z |
| publishDate | 2015-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-be87475b14094c5995530e5f7727914d2022-12-22T04:22:52ZengMDPI AGEntropy1099-43002015-09-011796213622810.3390/e17096213e17096213Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical SubmersionsAlina-Daniela Vîlcu0Gabriel-Eduard Vîlcu1Department of Computer Science, Information Technology, Mathematics and Physics, Petroleum-GasUniversity of Ploieᶊti, Bd. Bucureᶊti 39, Ploieᶊti 100680, RomaniaResearch Center in Geometry, Topology and Algebra, Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, Sector 1, Bucharest 70109, RomaniaIn this paper we investigate statistical manifolds with almost quaternionic structures. We define the concept of quaternionic Kähler-like statistical manifold and derive the main properties of quaternionic Kähler-like statistical submersions, extending in a new setting some previous results obtained by K. Takano concerning statistical manifolds endowed with almost complex and almost contact structures. Finally, we give a nontrivial example and propose some open problems in the field for further research.http://www.mdpi.com/1099-4300/17/9/6213affine connectionconjugate connectionstatistical manifoldstatistical submersionalmost quaternionic structure |
| spellingShingle | Alina-Daniela Vîlcu Gabriel-Eduard Vîlcu Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical Submersions Entropy affine connection conjugate connection statistical manifold statistical submersion almost quaternionic structure |
| title | Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical Submersions |
| title_full | Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical Submersions |
| title_fullStr | Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical Submersions |
| title_full_unstemmed | Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical Submersions |
| title_short | Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical Submersions |
| title_sort | statistical manifolds with almost quaternionic structures and quaternionic kahler like statistical submersions |
| topic | affine connection conjugate connection statistical manifold statistical submersion almost quaternionic structure |
| url | http://www.mdpi.com/1099-4300/17/9/6213 |
| work_keys_str_mv | AT alinadanielavilcu statisticalmanifoldswithalmostquaternionicstructuresandquaternionickahlerlikestatisticalsubmersions AT gabrieleduardvilcu statisticalmanifoldswithalmostquaternionicstructuresandquaternionickahlerlikestatisticalsubmersions |