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http://dx.doi.org/10.4134/CKMS.c200001

CURVATURES OF SEMI-SYMMETRIC METRIC CONNECTIONS ON STATISTICAL MANIFOLDS  

Balgeshir, Mohammad Bagher Kazemi (Department of Mathematics University of Zanjan)
Salahvarzi, Shiva (Department of Mathematics University of Zanjan)
Publication Information
Communications of the Korean Mathematical Society / v.36, no.1, 2021 , pp. 149-164 More about this Journal
Abstract
By using a statistical connection, we define a semi-symmetric metric connection on statistical manifolds and study the geometry of these manifolds and their submanifolds. We show the symmetry properties of the curvature tensor with respect to the semi-symmetric metric connections. Also, we prove the induced connection on a submanifold with respect to a semi-symmetric metric connection is a semi-symmetric metric connection and the second fundamental form coincides with the second fundamental form of the Levi-Civita connection. Furthermore, we obtain the Gauss, Codazzi and Ricci equations with respect to the new connection. Finally, we construct non-trivial examples of statistical manifolds admitting a semi-symmetric metric connection.
Keywords
Semi-symmetric connection; statistical manifolds; curvature tensor;
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Times Cited By KSCI : 1  (Citation Analysis)
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