{"id":"https://openalex.org/W2728154867","doi":"https://doi.org/10.3390/sym9070112","title":"On Submanifolds in a Riemannian Manifold with a Semi-Symmetric Non-Metric Connection","display_name":"On Submanifolds in a Riemannian Manifold with a Semi-Symmetric Non-Metric Connection","publication_year":2017,"publication_date":"2017-07-07","ids":{"openalex":"https://openalex.org/W2728154867","doi":"https://doi.org/10.3390/sym9070112","mag":"2728154867"},"language":"en","primary_location":{"id":"doi:10.3390/sym9070112","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym9070112","pdf_url":"https://www.mdpi.com/2073-8994/9/7/112/pdf?version=1499735813","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/9/7/112/pdf?version=1499735813","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100336872","display_name":"Jing Li","orcid":"https://orcid.org/0000-0002-0540-0412"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Li","raw_affiliation_strings":["School of Science, Nanjing University of Science and Technology, Nanjing 210094, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Nanjing University of Science and Technology, Nanjing 210094, China","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101091970","display_name":"Guoqing He","orcid":null},"institutions":[{"id":"https://openalex.org/I4472751","display_name":"Anhui Normal University","ror":"https://ror.org/05fsfvw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I4472751"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guoqing He","raw_affiliation_strings":["School of Mathematics and Computer Science, AnHui Normal University, Wuhu 241000, China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computer Science, AnHui Normal University, Wuhu 241000, China;","institution_ids":["https://openalex.org/I4472751"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010268270","display_name":"Peibiao Zhao","orcid":"https://orcid.org/0000-0002-0262-5544"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peibiao Zhao","raw_affiliation_strings":["School of Science, Nanjing University of Science and Technology, Nanjing 210094, China"],"raw_orcid":"https://orcid.org/0000-0002-0262-5544","affiliations":[{"raw_affiliation_string":"School of Science, Nanjing University of Science and Technology, Nanjing 210094, China","institution_ids":["https://openalex.org/I36399199"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101091970"],"corresponding_institution_ids":["https://openalex.org/I4472751"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":3.8697,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.9375568,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"9","issue":"7","first_page":"112","last_page":"112"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12712","display_name":"Myofascial pain diagnosis and treatment","score":0.982699990272522,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9815999865531921,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metric-connection","display_name":"Metric connection","score":0.8694682121276855},{"id":"https://openalex.org/keywords/levi-civita-connection","display_name":"Levi-Civita connection","score":0.8692640662193298},{"id":"https://openalex.org/keywords/submanifold","display_name":"Submanifold","score":0.8572596311569214},{"id":"https://openalex.org/keywords/fundamental-theorem-of-riemannian-geometry","display_name":"Fundamental theorem of Riemannian geometry","score":0.8568730354309082},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.8387038707733154},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6800906658172607},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5811754465103149},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5579163432121277},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.5430206656455994},{"id":"https://openalex.org/keywords/statistical-manifold","display_name":"Statistical manifold","score":0.5335890054702759},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.5081608295440674},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.505500078201294},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5007119178771973},{"id":"https://openalex.org/keywords/pseudo-riemannian-manifold","display_name":"Pseudo-Riemannian manifold","score":0.49099186062812805},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.3719761371612549},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.32745426893234253},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.2779366970062256},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17795032262802124},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16226941347122192},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.07132360339164734}],"concepts":[{"id":"https://openalex.org/C76453154","wikidata":"https://www.wikidata.org/wiki/Q788494","display_name":"Metric connection","level":5,"score":0.8694682121276855},{"id":"https://openalex.org/C129049296","wikidata":"https://www.wikidata.org/wiki/Q548675","display_name":"Levi-Civita connection","level":5,"score":0.8692640662193298},{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.8572596311569214},{"id":"https://openalex.org/C4306028","wikidata":"https://www.wikidata.org/wiki/Q2185349","display_name":"Fundamental theorem of Riemannian geometry","level":4,"score":0.8568730354309082},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.8387038707733154},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6800906658172607},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5811754465103149},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5579163432121277},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.5430206656455994},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.5335890054702759},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.5081608295440674},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.505500078201294},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5007119178771973},{"id":"https://openalex.org/C121705324","wikidata":"https://www.wikidata.org/wiki/Q1510587","display_name":"Pseudo-Riemannian manifold","level":4,"score":0.49099186062812805},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.3719761371612549},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32745426893234253},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.2779366970062256},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17795032262802124},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16226941347122192},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.07132360339164734},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym9070112","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym9070112","pdf_url":"https://www.mdpi.com/2073-8994/9/7/112/pdf?version=1499735813","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:035e44d123884b51804ece3a07c53e80","is_oa":true,"landing_page_url":"https://doaj.org/article/035e44d123884b51804ece3a07c53e80","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 9, Iss 7, p 112 (2017)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/9/7/112/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym9070112","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 9; Issue 7; Pages: 112","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym9070112","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym9070112","pdf_url":"https://www.mdpi.com/2073-8994/9/7/112/pdf?version=1499735813","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.46000000834465027}],"awards":[{"id":"https://openalex.org/G7377266725","display_name":null,"funder_award_id":"11371194","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8235583917","display_name":"\u65e0\u9650\u7ef4Teichmuller\u7a7a\u95f4\u7d27\u5316\u7684\u76f8\u5173\u7814\u7a76","funder_award_id":"11571172","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2728154867.pdf","grobid_xml":"https://content.openalex.org/works/W2728154867.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W2031077010","https://openalex.org/W2093674859","https://openalex.org/W2111802396","https://openalex.org/W2256641230","https://openalex.org/W2378783562","https://openalex.org/W2419902935","https://openalex.org/W2728154867","https://openalex.org/W2942794965","https://openalex.org/W6717438881"],"related_works":["https://openalex.org/W2613657242","https://openalex.org/W2588772101","https://openalex.org/W3182776298","https://openalex.org/W2185696382","https://openalex.org/W2008030028","https://openalex.org/W1892514668","https://openalex.org/W2728154867","https://openalex.org/W1016242396","https://openalex.org/W2038935112","https://openalex.org/W3193123020"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"submanifolds":[5,55],"in":[6],"a":[7,11,22,37],"Riemannian":[8],"manifold":[9],"with":[10,39,56],"semi-symmetric":[12,26,43,60],"non-metric":[13,27,44,61],"connection.":[14,28,45,62],"We":[15,29,46],"prove":[16],"that":[17],"the":[18,31,42,48,59],"induced":[19],"connection":[20],"on":[21],"submanifold":[23,38],"is":[24],"also":[25],"consider":[30],"total":[32],"geodesicness":[33],"and":[34,51],"minimality":[35],"of":[36],"respect":[40,57],"to":[41,58],"obtain":[47],"Gauss,":[49],"Cadazzi,":[50],"Ricci":[52],"equations":[53],"for":[54]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
