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Open AccessArticle

α-Connections and a Symmetric Cubic Form on a Riemannian Manifold

Department of Mechanical Engineering and Intelligent Systems, Faculty of Engineering, Tohoku Gakuin University, Tagajo, Miyagi 985-8537, Japan
Entropy 2017, 19(7), 344; https://doi.org/10.3390/e19070344
Received: 9 May 2017 / Revised: 6 July 2017 / Accepted: 6 July 2017 / Published: 10 July 2017
(This article belongs to the Special Issue Information Geometry II)
In this paper, we study the construction of α -conformally equivalent statistical manifolds for a given symmetric cubic form on a Riemannian manifold. In particular, we describe a method to obtain α -conformally equivalent connections from the relation between tensors and the symmetric cubic form. View Full-Text
Keywords: information geometry; statistical manifold; affine geometry; α-connection; conformal equivalence information geometry; statistical manifold; affine geometry; α-connection; conformal equivalence
MDPI and ACS Style

Uohashi, K. α-Connections and a Symmetric Cubic Form on a Riemannian Manifold. Entropy 2017, 19, 344.

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