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

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Department of Computer Science, Information Technology, Mathematics and Physics, Petroleum-GasUniversity of Ploieᶊti, Bd. Bucureᶊti 39, Ploieᶊti 100680, Romania
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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
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Kevin H. Knuth
Entropy 2015, 17(9), 6213-6228; https://doi.org/10.3390/e17096213
Received: 27 June 2015 / Revised: 31 August 2015 / Accepted: 1 September 2015 / Published: 7 September 2015
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
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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