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Entropy 2015, 17(9), 6213-6228; doi:10.3390/e17096213

Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical Submersions

1
Department of Computer Science, Information Technology, Mathematics and Physics, Petroleum-GasUniversity of Ploieᶊti, Bd. Bucureᶊti 39, Ploieᶊti 100680, Romania
2
Research Center in Geometry, Topology and Algebra, Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, Sector 1, Bucharest 70109, Romania
3
Department of Mathematical Modelling, Economic Analysis and Statistics, Petroleum-Gas Universityof Ploieᶊti, Bd. Bucureᶊti 39, Ploieᶊti 100680, Romania
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 27 June 2015 / Revised: 31 August 2015 / Accepted: 1 September 2015 / Published: 7 September 2015
View Full-Text   |   Download PDF [240 KB, uploaded 7 September 2015]

Abstract

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. View Full-Text
Keywords: affine connection; conjugate connection; statistical manifold; statistical submersion; almost quaternionic structure affine connection; conjugate connection; statistical manifold; statistical submersion; almost quaternionic structure
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Vîlcu, A.-D.; Vîlcu, G.-E. Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kähler-like Statistical Submersions. Entropy 2015, 17, 6213-6228.

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