Entropy (Jul 2018)

Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature

  • Simona Decu,
  • Stefan Haesen,
  • Leopold Verstraelen,
  • Gabriel-Eduard Vîlcu

DOI
https://doi.org/10.3390/e20070529
Journal volume & issue
Vol. 20, no. 7
p. 529

Abstract

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In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties. We establish some inequalities involving the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant). Moreover, we prove that the equality cases of the inequalities hold if and only if the imbedding curvature tensors h and h∗ of the submanifold (associated with the dual connections) satisfy h=−h∗, i.e., the submanifold is totally geodesic with respect to the Levi–Civita connection.

Keywords