{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:44:22Z","timestamp":1760233462890,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,5]],"date-time":"2021-01-05T00:00:00Z","timestamp":1609804800000},"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":["No.11771070."],"award-info":[{"award-number":["No.11771070."]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, the cases of non-integrable distributions in a Riemannian manifold with the first generalized semi-symmetric non-metric connection and the second generalized semi-symmetric non-metric connection are discussed. We obtain the Gauss, Codazzi, and Ricci equations in both cases. Moreover, Chen\u2019s inequalities are also obtained in both cases. Some new examples based on non-integrable distributions in a Riemannian manifold with generalized semi-symmetric non-metric connections are proposed.<\/jats:p>","DOI":"10.3390\/sym13010079","type":"journal-article","created":{"date-parts":[[2021,1,5]],"date-time":"2021-01-05T11:51:39Z","timestamp":1609847499000},"page":"79","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generalized Semi-Symmetric Non-Metric Connections of Non-Integrable Distributions"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7318-7564","authenticated-orcid":false,"given":"Tong","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,5]]},"reference":[{"key":"ref_1","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":"Proc. 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