{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T14:13:55Z","timestamp":1775225635345,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T00:00:00Z","timestamp":1580428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We establish Chen inequality for the invariant     \u03b4 ( 2 , 2 )     on statistical submanifolds in Hessian manifolds of constant Hessian curvature. Recently, in co-operation with Chen, we proved a Chen first inequality for such submanifolds. The present authors previously initiated the investigation of statistical submanifolds in Hessian manifolds of constant Hessian curvature; this paper represents a development in this topic.<\/jats:p>","DOI":"10.3390\/e22020164","type":"journal-article","created":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T11:55:56Z","timestamp":1580471756000},"page":"164","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["The \u03b4(2,2)-Invariant on Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature"],"prefix":"10.3390","volume":"22","author":[{"given":"Adela","family":"Mihai","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3782-2983","authenticated-orcid":false,"given":"Ion","family":"Mihai","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Amari, S. 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