Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2022; 37(3): 851-864

Online first article December 30, 2021      Printed July 31, 2022

https://doi.org/10.4134/CKMS.c210185

Copyright © The Korean Mathematical Society.

Chen invariants and statistical submanifolds

Hitoshi Furuhata, Izumi Hasegawa, 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 manifold, statistical submanifold, sectional curvature, $delta$-invariant

MSC numbers: Primary 53B25, 53C15