{"id":"https://openalex.org/W4404045433","doi":"https://doi.org/10.3390/sym16111463","title":"Application of Differential Equations on the Ricci Curvature of Contact CR-Warped Product Submanifolds of S2n+1(1) with Semi-Symmetric Metric Connection","display_name":"Application of Differential Equations on the Ricci Curvature of Contact CR-Warped Product Submanifolds of S2n+1(1) with Semi-Symmetric Metric Connection","publication_year":2024,"publication_date":"2024-11-04","ids":{"openalex":"https://openalex.org/W4404045433","doi":"https://doi.org/10.3390/sym16111463"},"language":"en","primary_location":{"id":"doi:10.3390/sym16111463","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16111463","pdf_url":"https://www.mdpi.com/2073-8994/16/11/1463/pdf?version=1730783901","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/2073-8994/16/11/1463/pdf?version=1730783901","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030826658","display_name":"Meraj Ali Khan","orcid":"https://orcid.org/0000-0001-6554-1228"},"institutions":[{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Meraj Ali Khan","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-6554-1228","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075506970","display_name":"Amira A. Ishan","orcid":"https://orcid.org/0000-0002-1729-4805"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Amira A. Ishan","raw_affiliation_strings":["Department of Mathematics, College of Science, Taif University, Taif 21944, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-1729-4805","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Taif University, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006916462","display_name":"Ibrahim Al-Dayel","orcid":"https://orcid.org/0000-0002-5901-2511"},"institutions":[{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ibrahim Al-Dayel","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089381721","display_name":"Khalid Masood","orcid":"https://orcid.org/0000-0002-5927-2807"},"institutions":[{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Khalid Masood","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5030826658"],"corresponding_institution_ids":["https://openalex.org/I240666556"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31467763,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"11","first_page":"1463","last_page":"1463"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9995999932289124,"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":0.9995999932289124,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9930999875068665,"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"}},{"id":"https://openalex.org/T12351","display_name":"Geometry and complex manifolds","score":0.9781000018119812,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/submanifold","display_name":"Submanifold","score":0.8653855323791504},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.7956883311271667},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6938468217849731},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.6380929946899414},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.6110112071037292},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.581167995929718},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5689456462860107},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5073789954185486},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.5005190372467041},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4750252366065979},{"id":"https://openalex.org/keywords/riemann-curvature-tensor","display_name":"Riemann curvature tensor","score":0.4734637141227722},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.44683367013931274},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17215362191200256},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16620105504989624}],"concepts":[{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.8653855323791504},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.7956883311271667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6938468217849731},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6380929946899414},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.6110112071037292},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.581167995929718},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5689456462860107},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5073789954185486},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.5005190372467041},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4750252366065979},{"id":"https://openalex.org/C183517385","wikidata":"https://www.wikidata.org/wiki/Q855112","display_name":"Riemann curvature tensor","level":3,"score":0.4734637141227722},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.44683367013931274},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17215362191200256},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16620105504989624},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16111463","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16111463","pdf_url":"https://www.mdpi.com/2073-8994/16/11/1463/pdf?version=1730783901","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:50d05621dc6e4568887f9e8ad6fbbdd2","is_oa":false,"landing_page_url":"https://doaj.org/article/50d05621dc6e4568887f9e8ad6fbbdd2","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 11, p 1463 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16111463","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16111463","pdf_url":"https://www.mdpi.com/2073-8994/16/11/1463/pdf?version=1730783901","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":[],"awards":[{"id":"https://openalex.org/G3521040092","display_name":null,"funder_award_id":"IMSIU-RP23036","funder_id":"https://openalex.org/F4320325415","funder_display_name":"Al-Imam Muhammad Ibn Saud Islamic University"}],"funders":[{"id":"https://openalex.org/F4320325415","display_name":"Al-Imam Muhammad Ibn Saud Islamic University","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4404045433.pdf","grobid_xml":"https://content.openalex.org/works/W4404045433.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W3103301","https://openalex.org/W1528265664","https://openalex.org/W1876490078","https://openalex.org/W1972444430","https://openalex.org/W1988739256","https://openalex.org/W1990777539","https://openalex.org/W2020384646","https://openalex.org/W2027430785","https://openalex.org/W2031077010","https://openalex.org/W2038659849","https://openalex.org/W2051983384","https://openalex.org/W2062346296","https://openalex.org/W2065025740","https://openalex.org/W2069261787","https://openalex.org/W2076228339","https://openalex.org/W2084396992","https://openalex.org/W2115131806","https://openalex.org/W2137697813","https://openalex.org/W2335251188","https://openalex.org/W2604945298","https://openalex.org/W2872907760","https://openalex.org/W2908633068","https://openalex.org/W2942794965","https://openalex.org/W2946363963","https://openalex.org/W2973024465","https://openalex.org/W3010739584","https://openalex.org/W3032223079","https://openalex.org/W4390755140","https://openalex.org/W6647871971","https://openalex.org/W6668257444","https://openalex.org/W6680422606"],"related_works":["https://openalex.org/W2080150912","https://openalex.org/W4250961967","https://openalex.org/W2058655323","https://openalex.org/W2024803319","https://openalex.org/W2254577414","https://openalex.org/W2946879650","https://openalex.org/W2604503417","https://openalex.org/W2087358568","https://openalex.org/W2088076227","https://openalex.org/W4387382666"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,28,45],"explore":[4],"the":[5,14,34,47,65],"uses":[6],"of":[7,17,49,75],"Obata\u2019s":[8],"differential":[9,51],"equation":[10],"in":[11],"relation":[12],"to":[13],"Ricci":[15],"curvature":[16],"an":[18,41],"odd-dimensional":[19],"sphere":[20],"that":[21],"possesses":[22],"a":[23,72],"semi-symmetric":[24],"metric":[25],"connection.":[26],"Specifically,":[27],"establish":[29],"that,":[30,58],"given":[31],"certain":[32,60],"conditions,":[33],"underlying":[35],"submanifold":[36,67],"can":[37,68],"be":[38,69],"identified":[39],"as":[40,71],"isometric":[42],"sphere.":[43],"Additionally,":[44],"investigate":[46],"impact":[48],"specific":[50],"equations":[52],"on":[53],"these":[54],"submanifolds":[55],"and":[56],"demonstrate":[57],"when":[59],"geometric":[61],"conditions":[62],"are":[63],"met,":[64],"base":[66],"characterized":[70],"special":[73],"type":[74],"warped":[76],"product.":[77]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
