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Inequalities on Sasakian Statistical Manifolds in Terms of Casorati Curvatures

Author

Listed:
  • Chul Woo Lee

    (Department of Mathematics, Kyungpook National University, Daegu 41566, Korea)

  • Jae Won Lee

    (Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Korea)

Abstract

A statistical structure is considered as a generalization of a pair of a Riemannian metric and its Levi-Civita connection. With a pair of conjugate connections ∇ and ∇ * in the Sasakian statistical structure, we provide the normalized scalar curvature which is bounded above from Casorati curvatures on C -totally real (Legendrian and slant) submanifolds of a Sasakian statistical manifold of constant φ -sectional curvature. In addition, we give examples to show that the total space is a sphere.

Suggested Citation

  • Chul Woo Lee & Jae Won Lee, 2018. "Inequalities on Sasakian Statistical Manifolds in Terms of Casorati Curvatures," Mathematics, MDPI, vol. 6(11), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:259-:d:183603
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    References listed on IDEAS

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    1. Paul Vos, 1989. "Fundamental equations for statistical submanifolds with applications to the Bartlett correction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(3), pages 429-450, September.
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    Cited by:

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