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 Chen invariants and statistical submanifolds Commun. Korean Math. Soc.Published online December 30, 2021 Hitoshi Furuhata, Izumi Hasegawa, and Naoto Satoh Hokkaido University; Hokkaido University of Education; National Institute of Technology, Asahikawa College Abstract : We define a kind of sectional curvature and $\delta$-invariants for statistical manifolds. For statistical submanifolds the sum of the squared mean curvature and the squared dual mean curvature is bounded below by using the $\delta$-invariant. This inequality can be considered as a generalization of the so-called Chen inequality for Riemannian submanifolds. Keywords : statistical submanifold MSC numbers : 53B25 Full-Text :

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