{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T01:34:45Z","timestamp":1775093685075,"version":"3.50.1"},"reference-count":12,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,8]],"date-time":"2017-07-08T00:00:00Z","timestamp":1499472000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we study submanifolds in a Riemannian manifold with a semi-symmetric non-metric connection. We prove that the induced connection on a submanifold is also semi-symmetric non-metric connection. We consider the total geodesicness and minimality of a submanifold with respect to the semi-symmetric non-metric connection. We obtain the Gauss, Cadazzi, and Ricci equations for submanifolds with respect to the semi-symmetric non-metric connection.<\/jats:p>","DOI":"10.3390\/sym9070112","type":"journal-article","created":{"date-parts":[[2017,7,7]],"date-time":"2017-07-07T10:37:17Z","timestamp":1499423837000},"page":"112","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["On Submanifolds in a Riemannian Manifold with a Semi-Symmetric Non-Metric Connection"],"prefix":"10.3390","volume":"9","author":[{"given":"Jing","family":"Li","sequence":"first","affiliation":[{"name":"School of Science, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guoqing","family":"He","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, AnHui Normal University, Wuhu 241000, China;"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0262-5544","authenticated-orcid":false,"given":"Peibiao","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Science, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/BF01187468","article-title":"\u00dcber die Geometrie der halbsymmetrischen \u00dcbertragungen","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":"Proc. Lond. Math. Soc."},{"key":"ref_3","first-page":"1579","article-title":"On semi-symmetric metric connection","volume":"15","author":"Yano","year":"1970","journal-title":"Rev. Roum. Math. Pures Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1090\/S0002-9939-1976-0445416-9","article-title":"Submanifolds of a Riemanian with semi-symmetric metric connections","volume":"54","author":"Nakao","year":"1976","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_5","first-page":"157","article-title":"Pseudo metric semi-symmetric connections","volume":"18","author":"Prvanovic","year":"1975","journal-title":"Publ. l\u2019Institut Math. 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