{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:32:51Z","timestamp":1760059971341,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T00:00:00Z","timestamp":1753315200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Foundation for Science and Technology","award":["LA\/P\/0112\/2020","UIDB\/00147\/2020","UIDP\/00147\/2020","C00L03ES310120220002"],"award-info":[{"award-number":["LA\/P\/0112\/2020","UIDB\/00147\/2020","UIDP\/00147\/2020","C00L03ES310120220002"]}]},{"name":"\u00c9cole Nationale Polytechnique d\u2019Oran","award":["LA\/P\/0112\/2020","UIDB\/00147\/2020","UIDP\/00147\/2020","C00L03ES310120220002"],"award-info":[{"award-number":["LA\/P\/0112\/2020","UIDB\/00147\/2020","UIDP\/00147\/2020","C00L03ES310120220002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper is about a problem at the intersection of differential geometry, spectral analysis and the theory of manifolds. The study of finite-type subvarieties was initiated by Chen in the 1970s, with the aim of obtaining improved estimates for the mean total curvature of compact subvarieties in Euclidean space. The concept of a finite-type subvariety naturally extends that of a minimal subvariety or surface, the latter being closely related to variational calculus. In this work, we classify factorable surfaces in the Lorentz\u2013Heisenberg space H3, equipped with a flat metric satisfying \u0394Iri=\u03bbiri, which satisfies algebraic equations involving coordinate functions and the Laplacian operator with respect to the surface\u2019s first fundamental form.<\/jats:p>","DOI":"10.3390\/axioms14080568","type":"journal-article","created":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T14:11:44Z","timestamp":1753366304000},"page":"568","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Factorable Surfaces of Finite Chen Type in the Lorentz\u2013Heisenberg Space H3"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4554-105X","authenticated-orcid":false,"given":"Brahim","family":"Medjahdi","sequence":"first","affiliation":[{"name":"Ecole Normale Superieure D\u2019Oran Ammour Ahmed, Oran 31000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2061-1581","authenticated-orcid":false,"given":"Rafik","family":"Medjati","sequence":"additional","affiliation":[{"name":"Department of Preparatory Training in Science and Technology, Ecole Nationale Polytechnique d\u2019Oran\u2014Maurice Audin, B.P 1523 EL M\u2019naouar, Oran 31000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7247-3056","authenticated-orcid":false,"given":"Hanifi","family":"Zoubir","sequence":"additional","affiliation":[{"name":"Department of Preparatory Training in Science and Technology, Ecole Nationale Polytechnique d\u2019Oran\u2014Maurice Audin, B.P 1523 EL M\u2019naouar, Oran 31000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4272-6232","authenticated-orcid":false,"given":"Abdelkader","family":"Belhenniche","sequence":"additional","affiliation":[{"name":"SYSTEC-ARISE Research Center for Systems and Technologies, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias s\/n, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5179-4344","authenticated-orcid":false,"given":"Roman","family":"Chertovskih","sequence":"additional","affiliation":[{"name":"SYSTEC-ARISE Research Center for Systems and Technologies, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias s\/n, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, B.-Y. (1984). Total Mean Curvature and Submanifolds of Finite Type, World Scientific.","DOI":"10.1142\/0065"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"380","DOI":"10.2969\/jmsj\/01840380","article-title":"Minimal immersions of Riemannian manifolds","volume":"18","author":"Takahashi","year":"1966","journal-title":"J. Math. Soc. Jpn."},{"key":"ref_3","first-page":"1355","article-title":"Some classification of translation surfaces in Galilean 3-space","volume":"6","author":"Yoon","year":"2012","journal-title":"Int. J. Math. Anal."},{"key":"ref_4","first-page":"366","article-title":"Affine factorable surfaces in the three-dimensional simply isotropic space","volume":"51","author":"Medjahdi","year":"2021","journal-title":"IAENG Int. J. Appl. Math."},{"key":"ref_5","first-page":"154","article-title":"Classification of space-like translation surfaces in the 3-dimensional Lorentz Heisenberg group H3","volume":"29","author":"Medjati","year":"2023","journal-title":"Arab J. Math. 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Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"155","DOI":"10.4134\/BKMS.2009.46.1.155","article-title":"Factorable surfaces in 3-Minkowski space","volume":"46","author":"Meng","year":"2009","journal-title":"Bull. Korean Math. Soc."},{"key":"ref_11","first-page":"200","article-title":"Maximal and minimal surfaces of factorable surfaces in Heis3","volume":"3","author":"Turhan","year":"2010","journal-title":"Int. J. Open Probl. Comput. Sci. Math."},{"key":"ref_12","unstructured":"Yu, Y., and Liu, H. (2007). The factorable minimal surfaces. Proceedings of the Eleventh International Workshop on Differential Geometry, Kyungpook National University."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/8\/568\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:15:32Z","timestamp":1760033732000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/8\/568"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,24]]},"references-count":12,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["axioms14080568"],"URL":"https:\/\/doi.org\/10.3390\/axioms14080568","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,7,24]]}}}