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.