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Mathematics 2019, 7(1), 104; https://doi.org/10.3390/math7010104

Completness of Statistical Structures

Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Cracow, Poland
Received: 30 November 2018 / Revised: 8 January 2019 / Accepted: 11 January 2019 / Published: 19 January 2019
(This article belongs to the Special Issue Differential Geometry)
Full-Text   |   PDF [214 KB, uploaded 22 January 2019]

Abstract

In this survey note, we discuss the notion of completeness for statistical structures. There are at least three connections whose completeness might be taken into account, namely, the Levi-Civita connection of the given metric, the statistical connection, and its conjugate. Especially little is known on the completeness of statistical connections. View Full-Text
Keywords: statistical structure; affine hypersurface; affine sphere; conjugate symmetric statistical structure; sectional ∇-curvature; complete connection statistical structure; affine hypersurface; affine sphere; conjugate symmetric statistical structure; sectional ∇-curvature; complete connection
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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Opozda, B. Completness of Statistical Structures. Mathematics 2019, 7, 104.

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