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

Autor:	Simona Decu, Stefan Haesen, Leopold Verstraelen, Gabriel-Eduard Vîlcu
Jazyk:	angličtina
Rok vydání:	2018
Předmět:	casorati curvature statistical submanifold Kenmotsu statistical manifold dual connections Science Astrophysics QB460-466 Physics QC1-999
Zdroj:	Entropy, Vol 20, Iss 7, p 529 (2018)
Druh dokumentu:	article
ISSN:	1099-4300
DOI:	10.3390/e20070529
Popis:	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.
Databáze:	Directory of Open Access Journals
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