{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T13:21:41Z","timestamp":1771939301773,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T00:00:00Z","timestamp":1771200000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Imam Mohammad Ibn Saud Islamic University","award":["IMSIU-DDRSP2602"],"award-info":[{"award-number":["IMSIU-DDRSP2602"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we undertake a detailed study of pseudoparallel submanifolds of almost Kenmotsu (\u03ba,\u03bc,\u03bd)-spaces, with particular emphasis on invariant submanifolds. By employing the W0 and W1 curvature tensors, we analyze several classes of pseudoparallel submanifolds, including Ricci-generalized pseudoparallel ones, and investigate how these curvature conditions influence the intrinsic and extrinsic geometry of the submanifolds. One of the main contributions of this work is the derivation of necessary and sufficient conditions under which invariant pseudoparallel submanifolds of almost Kenmotsu (\u03ba,\u03bc,\u03bd)-spaces become totally geodesic. In particular, the use of the W0 and W1 curvature tensors provides a unified and effective framework for characterizing total geodesicity in this geometric setting. Furthermore, we obtain new and significant classification results by explicitly relating the total geodesicity of invariant submanifolds to the structural functions \u03ba,\u00a0\u03bc and \u03bd. These results not only generalize several known characterizations in the literature but also yield novel geometric insights into the structure of pseudoparallel submanifolds in almost Kenmotsu (\u03ba,\u03bc,\u03bd)-spaces. We also provide an example to support our concept.<\/jats:p>","DOI":"10.3390\/axioms15020146","type":"journal-article","created":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T12:37:28Z","timestamp":1771245448000},"page":"146","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Intrinsic and Extrinsic Geometry of Pseudoparallel Submanifolds in Almost Kenmotsu (\u03ba, \u03bc, \u03bd)-Manifolds"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5901-2511","authenticated-orcid":false,"given":"Ibrahim","family":"Al-Dayel","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8258-8298","authenticated-orcid":false,"given":"Tu\u011fba","family":"Mert","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Sivas Cumhuriyet, Sivas 58140, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1713-6831","authenticated-orcid":false,"given":"Mohd Danish","family":"Siddiqi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 4512, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s13370-018-0631-z","article-title":"Certain results on N(k)-quasi Einstein manifolds","volume":"30","author":"Chaubey","year":"2019","journal-title":"Afr. Mat."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"36069","DOI":"10.3934\/math.20241711","article-title":"Schur-type inequality for solitonic hypersurfaces in (\u03ba, \u03bc)-contact metric manifolds","volume":"9","author":"Siddiqi","year":"2024","journal-title":"AIMS Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"145","DOI":"10.5269\/bspm.41450","article-title":"Existence of some classes of N(k)-quasi Einstein manifolds","volume":"39","author":"Chaubey","year":"2021","journal-title":"Bol. Soc. Paran. 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