Curvatures of semi-symmetric metric connections on statistical manifolds
Commun. Korean Math. Soc. 2021 Vol. 36, No. 1, 149-164
Published online November 11, 2020
Printed January 31, 2021
Mohammad Bagher Kazemi Balgeshir, Shiva Salahvarzi
P.O. Box 45371-38791; P.O. Box 45371-38791
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
MSC numbers : Primary 53B25, 53C07, 60D05
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