{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T20:46:27Z","timestamp":1764103587769,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T00:00:00Z","timestamp":1740009600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The focus of this research is on investigating a new category of generalized symmetric metric connections within nearly Kenmotsu manifolds. The study delves into recognizing the generalized symmetric connections of type (\u03b1,\u00a0\u03b2), which represent broader versions of the semi-symmetric metric connection (\u03b1=1,\u00a0\u03b2=0) and the quarter-symmetric metric connection (\u03b1=0,\u00a0\u03b2=1).<\/jats:p>","DOI":"10.3390\/sym17030317","type":"journal-article","created":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T04:53:39Z","timestamp":1740027219000},"page":"317","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Study of Generalized Symmetric Metric Connection on Nearly Kenmotsu Manifolds"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6779-4883","authenticated-orcid":false,"given":"Rajesh","family":"Kumar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Pachhunga University College, Mizoram University, Aizawl 796001, Mizoram, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-1727-5353","authenticated-orcid":false,"given":"Laltluangkima","family":"Chawngthu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Mizoram University, Tanhril, Aizawl 796004, Mizoram, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5054-8865","authenticated-orcid":false,"given":"O\u011fuzhan","family":"Bahadir","sequence":"additional","affiliation":[{"name":"Faculty of Sciences, Kahramanmaras Sutcu Imam University, Kahramanmaras 46100, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6554-1228","authenticated-orcid":false,"given":"Meraj Ali","family":"Khan","sequence":"additional","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"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/BF01187468","article-title":"\u00dcber die Geometrie der halbsymmetrischen \u00dcbertragung","volume":"21","author":"Friedmann","year":"1924","journal-title":"Math. Z."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1112\/plms\/s2-34.1.27","article-title":"Subspaces of a space with torsion","volume":"34","author":"Hayden","year":"1932","journal-title":"Lond. Math. Soc."},{"key":"ref_3","first-page":"249","article-title":"On semi-symmetric and quarter-symmetric linear connections","volume":"29","author":"Golab","year":"1975","journal-title":"Tensor New Ser."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Li, Y., Mallick, A.K., Bhattacharyya, A., and Stankovic, M.S. (2024). A Conformal \u03b7-Ricci Soliton on a Four-Dimensional Lorentzian Para-Sasakian Manifold. Axioms, 13.","DOI":"10.3390\/axioms13110753"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Li, Y., Siddesha, M.S., Kumara, H.A., and Praveena, M.M. (2024). Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds. Mathematics, 12.","DOI":"10.3390\/math12193130"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"20240063","DOI":"10.1515\/math-2024-0063","article-title":"Riemannian invariants for warped product submanifolds in Q\u03f5m\u00d7R and their applications","volume":"22","author":"Li","year":"2024","journal-title":"Open Math."},{"key":"ref_7","first-page":"399","article-title":"A semi symetric non-metric connection in a Riemannian manifold","volume":"23","author":"Agashe","year":"1992","journal-title":"Indian J. Pure Appl. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1887","DOI":"10.3906\/mat-1902-2","article-title":"Riemannian manifolds admitting a new type of semi-symmetric non-metric connection","volume":"43","author":"Chaubey","year":"2019","journal-title":"Turk. J. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"63","DOI":"10.2298\/FIL1202269C","article-title":"On a semi-symmetric non-metric connection","volume":"26","author":"Chaubey","year":"2012","journal-title":"Filomat"},{"key":"ref_10","first-page":"1113","article-title":"Riemannian manifolds with a semi-symmetric metric P-connection","volume":"56","author":"Chaubey","year":"2019","journal-title":"J. Korean Math. Soc."},{"key":"ref_11","first-page":"707","article-title":"Hypersurfaces of Riemannian manifold with semi-symmetric non-metric connection","volume":"75","author":"De","year":"1995","journal-title":"J. Indian Inst. Sci."},{"key":"ref_12","first-page":"107","article-title":"On semi-symmetric recurrent-metric connection","volume":"55","author":"Liang","year":"1994","journal-title":"Tensor New Ser."},{"key":"ref_13","first-page":"202","article-title":"On semi-symmetric non-metric and quarter-symmetric metric connections","volume":"70","author":"Chaubey","year":"2008","journal-title":"Tensor New Ser."},{"key":"ref_14","first-page":"15","article-title":"A new connection in a Riemannian manifold","volume":"1","author":"Tripathi","year":"2006","journal-title":"Int. Electron. J. Geom."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.3906\/mat-1207-38","article-title":"On nearly Kenmotsu manifolds","volume":"37","author":"Najafi","year":"2013","journal-title":"Turk. J. Math."},{"key":"ref_16","first-page":"131","article-title":"On nearly Kenmotsu manifolds with semi-symmetric metric connection","volume":"68","author":"Prasad","year":"2018","journal-title":"GANITA"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Blair, D.E. (2010). Riemannian geometry of contact and symplectic manifolds. Progress in Mathematics, Birkhauser.","DOI":"10.1007\/978-0-8176-4959-3"},{"key":"ref_18","first-page":"139","article-title":"Nearly trans-Sasakian manifolds","volume":"23","author":"Shukla","year":"1996","journal-title":"Kuwait J. Sci. Eng."},{"key":"ref_19","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_20","first-page":"1","article-title":"On semi-invariant submanifolds of a nearly Kenmotsu manifold with a quarter symmetric non-metric connection","volume":"18","author":"Mobin","year":"2011","journal-title":"J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math."},{"key":"ref_21","first-page":"461","article-title":"Some notes on LP-Sasakian manifolds with generalized symmetric metric connection","volume":"42","author":"Bahadir","year":"2020","journal-title":"Honam Math. J."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Prakasha, D.G., Turki, N.B., Deepika, M.V., and \u00dcnal, \u0130. (2024). On LP-Kenmotsu manifold with regard to generalized symmetric metric connection of type (\u03b1, \u03b2). Mathematics, 12.","DOI":"10.3390\/math12182915"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Choudhary, M.A., Khedher, K.M., Bahadir, O., and Siddiqi, M.D. (2021). On Golden Lorentzian manifolds equipped with generalized symmetric metric connection. Mathematics, 9.","DOI":"10.3390\/math9192430"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"75","DOI":"10.30755\/NSJOM.11016","article-title":"LP-Sasakian manifolds with generalized symmetric metric connection","volume":"51","author":"Bahadir","year":"2021","journal-title":"Novi Sad J. Math."},{"key":"ref_25","first-page":"97","article-title":"Curvature tensor and their relativistic significance II","volume":"19","author":"Pokhariyal","year":"1971","journal-title":"Yokohama Math. J."},{"key":"ref_26","first-page":"47","article-title":"On \u03d5-Ricci symmetric Sasakian manifolds","volume":"11","author":"De","year":"2008","journal-title":"Proc. Jangjeon Math. Soc."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/317\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:38:36Z","timestamp":1760027916000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/317"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,20]]},"references-count":26,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["sym17030317"],"URL":"https:\/\/doi.org\/10.3390\/sym17030317","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,2,20]]}}}