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http://hdl.handle.net/1942/28170
Title: | Curvature invariants of statistical submanifolds in Kenmotsu statistical manifolds of constant phi-sectional curvature | Authors: | Decu, Simona HAESEN, Stefan Verstraelen, Leopold Vilcu, Gabriel-Eduard |
Issue Date: | 2018 | Source: | Entropy, 20(7) (Art N° 529) | Abstract: | 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: | casorati curvature; statistical submanifold; Kenmotsu statistical manifold; dual connections | Document URI: | http://hdl.handle.net/1942/28170 | e-ISSN: | 1099-4300 | DOI: | 10.3390/e20070529 | ISI #: | 000440017100049 | Rights: | Copyright 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2019 |
Appears in Collections: | Research publications |
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entropy-20-00529.pdf | Published version | 288.46 kB | Adobe PDF | View/Open |
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