{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:01:54Z","timestamp":1760058114387,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T00:00:00Z","timestamp":1741824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Khalid University","award":["R.G.P.2\/03\/46","PNURSP2025R27"],"award-info":[{"award-number":["R.G.P.2\/03\/46","PNURSP2025R27"]}]},{"name":"Princess Nourah bint Abdulrahman University","award":["R.G.P.2\/03\/46","PNURSP2025R27"],"award-info":[{"award-number":["R.G.P.2\/03\/46","PNURSP2025R27"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper investigates the relationship between homology groups and warped product semi-slant submanifolds in Kenmotsu space forms. Some rigidity theorems for vanishing homology groups on warped product semi-slant submanifolds are obtained using the moving-frame method and the second fundamental form inequality. Our results are an extension of previous studies in this direction.<\/jats:p>","DOI":"10.3390\/axioms14030210","type":"journal-article","created":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T06:53:00Z","timestamp":1741848780000},"page":"210","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Trivial Homology Groups of Warped Product Semi-Slant Submanifolds in Kenmotsu Space Forms"],"prefix":"10.3390","volume":"14","author":[{"given":"Noura M.","family":"Alhouiti","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, University College of Haqel, University of Tabuk, Tabuk 71491, Saudi Arabia"}]},{"given":"Ali H.","family":"Alkhaldi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6053-3031","authenticated-orcid":false,"given":"Akram","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2116-7382","authenticated-orcid":false,"given":"Fatemah","family":"Mofarreh","sequence":"additional","affiliation":[{"name":"Mathematical Science Department, Faculty of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11546, Saudi Arabia"}]},{"given":"Piscoran","family":"Laurian-Ioan","sequence":"additional","affiliation":[{"name":"North University Center of Baia Mare, Department of Mathematics and Computer Science, Technical University of Cluj Napoca, Victoriei 76, 430122 Baia Mare, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"458","DOI":"10.2307\/1970227","article-title":"Normal and integral currents","volume":"72","author":"Federer","year":"1960","journal-title":"Ann. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"215","DOI":"10.4134\/BKMS.2015.52.1.215","article-title":"Homology of contact CR-warped product submanifolds of an odd-dimensional unit sphere","volume":"52","year":"2015","journal-title":"Bull. Korean Math. Soc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"427","DOI":"10.2307\/1970913","article-title":"On stable currents and their application to global problems in real and complex geometry","volume":"98","author":"Lawson","year":"1973","journal-title":"Ann. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2607","DOI":"10.1090\/S0002-9939-07-08901-0","article-title":"Homology vanishing theorems for submanifolds","volume":"135","author":"Vlachos","year":"2007","journal-title":"Proc. Amer. Math. Soc."},{"key":"ref_5","first-page":"233","article-title":"An application of integral currents to the vanishing theorems","volume":"27","author":"Xin","year":"1984","journal-title":"Sci. Sin. Ser. A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1850032","DOI":"10.1142\/S0219887818500329","article-title":"On the topology of CR-warped product submanifolds","volume":"15","year":"2018","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103471","DOI":"10.1016\/j.geomphys.2019.07.002","article-title":"Homology of submanifolds of the six-dimensional sphere","volume":"145","year":"2019","journal-title":"J. Geom. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2050121","DOI":"10.1142\/S0219887820501212","article-title":"Homology of warped product submanifolds in the unit sphere and its applications","volume":"17","author":"Ali","year":"2020","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1142\/S0129167X0800490X","article-title":"Vanishing and topological sphere theorems for submanifolds in a hyperbolic space","volume":"19","author":"Fu","year":"2008","journal-title":"Int. J. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"103566","DOI":"10.1016\/j.geomphys.2019.103566","article-title":"Stable currents and homology groups in a compact CR-warped product submanifold with negative constant sectional curvature","volume":"148","author":"Ali","year":"2020","journal-title":"J. Geom. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2050094","DOI":"10.1142\/S0219887820500942","article-title":"The normalized Ricci flow and homology in Lagrangian submanifolds of generalized complex space forms","volume":"17","author":"Fatemah","year":"2020","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7105","DOI":"10.2298\/FIL2321105K","article-title":"Analysis of stable currents and homology of biwarped product submanifolds in the Euclidean space","volume":"37","author":"Khan","year":"2023","journal-title":"Filomat"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"103859","DOI":"10.1016\/j.geomphys.2020.103859","article-title":"Null homology in warped product Lagrangian submanifolds of the nearly Kaehler S6 and its applications","volume":"158","author":"Ali","year":"2020","journal-title":"J. Geom. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Al-Dayel, I., and Khan, M.A. (2023). Impact of semi-symmetric metric connection on the homology of warped product pointwise semi-slant submanifolds of an odd-dimensional Sphere. Symmetry, 15.","DOI":"10.3390\/sym15081606"},{"key":"ref_15","first-page":"5035740","article-title":"Homology of warped product semi-invariant submanifolds of a Sasakian space form with the semi-symmetric metric connection","volume":"8","author":"Khan","year":"2023","journal-title":"J. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"93","DOI":"10.2748\/tmj\/1178241594","article-title":"A class of almost contact Riemannian manifolds","volume":"24","author":"Kenmotsu","year":"1972","journal-title":"Tohoku Math. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1007\/s13373-017-0106-9","article-title":"Geometry of warped product semi-slant submanifolds of Kenmotsu manifolds","volume":"8","author":"Uddin","year":"2018","journal-title":"Bull. Math. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/BF01766972","article-title":"A classification of almost contact metric manifolds","volume":"156","author":"Chinea","year":"1990","journal-title":"Ann. Mat. Pura Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1017\/S0017089500010156","article-title":"Slant submanifolds in Sasakian manifolds","volume":"42","author":"Cabrerizo","year":"2000","journal-title":"Glasg. Math. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1023\/A:1005241320631","article-title":"Semi-slant submanifolds of a Sasakian manifold","volume":"78","author":"Cabrerizo","year":"1999","journal-title":"Geom. Dedic."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9947-1969-0251664-4","article-title":"Manifolds of negative curvature","volume":"145","author":"Bishop","year":"1969","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_22","first-page":"319","article-title":"Warped product semi-slant submanifolds in Kenmotsu manifolds","volume":"36","author":"Atceken","year":"2012","journal-title":"Turk. J. Math."},{"key":"ref_23","first-page":"86","article-title":"Characterization of warped product submanifolds in Kenmotsu manifolds","volume":"20","author":"Mustafa","year":"2015","journal-title":"Balkan J. Geom. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"111267","DOI":"10.1016\/j.chaos.2021.111267","article-title":"Homology of contact 3-CR-submanifolds of an almost 3-contact hypersurface","volume":"151","year":"2021","journal-title":"Chaos Solitons Fractals"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3811","DOI":"10.2298\/FIL2111811S","article-title":"Homology of contact CR-submanifolds","volume":"35","author":"Sahin","year":"2021","journal-title":"Filomat"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/s41468-020-00057-9","article-title":"Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis","volume":"4","author":"Cang","year":"2020","journal-title":"J. Appl. Comput. Topol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"051102","DOI":"10.1063\/1.4983840","article-title":"Topological characterization and early detection of bifurcations and chaos in complex systems using persistent homology","volume":"27","author":"Mittal","year":"2017","journal-title":"Chaos"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/3\/210\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:53:00Z","timestamp":1760028780000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/3\/210"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,13]]},"references-count":27,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["axioms14030210"],"URL":"https:\/\/doi.org\/10.3390\/axioms14030210","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,3,13]]}}}