Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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CHEN INVARIANTS AND STATISTICAL SUBMANIFOLDS

  • Received : 2021.05.21
  • Accepted : 2021.10.14
  • Published : 2022.07.31
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Abstract

We define a kind of sectional curvature and 𝛿-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 𝛿-invariant. This inequality can be considered as a generalization of the so-called Chen inequality for Riemannian submanifolds.

Keywords

Acknowledgement

The authors wish to express their gratitude to Yukihiko Okuyama and Kimitake Sato for their kind help.

References

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