{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T22:22:28Z","timestamp":1774304548565,"version":"3.50.1"},"reference-count":55,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,11]],"date-time":"2022-09-11T00:00:00Z","timestamp":1662854400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101168"],"award-info":[{"award-number":["12101168"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["LQ22A010014"],"award-info":[{"award-number":["LQ22A010014"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12101168"],"award-info":[{"award-number":["12101168"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation of China","doi-asserted-by":"publisher","award":["LQ22A010014"],"award-info":[{"award-number":["LQ22A010014"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The paper undertakes certain special forms of the quarter symmetric metric and non-metric connections on an \u03b5-anti-K\u00e4hler manifold. Firstly, we deduce the relation between the Riemannian connection and the special forms of the quarter symmetric metric and non-metric connections. Then, we present some results concerning the torsion tensors of these connections. In addition, we find the forms of the curvature tensor, the Ricci curvature tensor and scalar curvature of such connections and we search the conditions for the \u03b5-anti-K\u00e4hler manifold to be an Einstein space with respect to these connections. Finally, we study U(Ric)-vector fields with respect to these connections and give some results related to them.<\/jats:p>","DOI":"10.3390\/sym14091899","type":"journal-article","created":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T22:37:28Z","timestamp":1663108648000},"page":"1899","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["E-Connections on the \u03b5-Anti-K\u00e4hler Manifolds"],"prefix":"10.3390","volume":"14","author":[{"given":"Zhizhi","family":"Chen","sequence":"first","affiliation":[{"name":"School of Statistics, Jilin University of Finance and Economics, Changchun 130117, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1614-3228","authenticated-orcid":false,"given":"Yanlin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aydin","family":"Gezer","sequence":"additional","affiliation":[{"name":"Faculty of Science, Department of Mathematics, Ataturk University, Erzurum 25240, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erkan","family":"Karakas","sequence":"additional","affiliation":[{"name":"Faculty of Science, Department of Mathematics, Ataturk University, Erzurum 25240, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6532-6317","authenticated-orcid":false,"given":"Cagri","family":"Karaman","sequence":"additional","affiliation":[{"name":"Faculty of Science, Department of Mathematics, Ataturk University, Erzurum 25240, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,11]]},"reference":[{"key":"ref_1","first-page":"249","article-title":"On semi-symmetric and quarter-symmetric linear connections","volume":"29","author":"Golab","year":"1975","journal-title":"Tensor (N. 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