{"id":"https://openalex.org/W4307633525","doi":"https://doi.org/10.3390/axioms11110594","title":"Conformal \u03b7-Ricci Solitons on Riemannian Submersions under Canonical Variation","display_name":"Conformal \u03b7-Ricci Solitons on Riemannian Submersions under Canonical Variation","publication_year":2022,"publication_date":"2022-10-27","ids":{"openalex":"https://openalex.org/W4307633525","doi":"https://doi.org/10.3390/axioms11110594"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11110594","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110594","pdf_url":"https://www.mdpi.com/2075-1680/11/11/594/pdf?version=1669106079","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/11/594/pdf?version=1669106079","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090554955","display_name":"Mohd Danish Siddiqi","orcid":"https://orcid.org/0000-0002-1713-6831"},"institutions":[{"id":"https://openalex.org/I91450128","display_name":"Jazan University","ror":"https://ror.org/02bjnq803","country_code":"SA","type":"education","lineage":["https://openalex.org/I91450128"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mohd. Danish Siddiqi","raw_affiliation_strings":["Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia","institution_ids":["https://openalex.org/I91450128"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054197686","display_name":"Ali H. Alkhaldi","orcid":"https://orcid.org/0000-0002-6562-4610"},"institutions":[{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Ali Hussain Alkhaldi","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, Abha 9004, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, Abha 9004, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030826658","display_name":"Meraj Ali Khan","orcid":"https://orcid.org/0000-0001-6554-1228"},"institutions":[{"id":"https://openalex.org/I72264486","display_name":"University of Tabuk","ror":"https://ror.org/04yej8x59","country_code":"SA","type":"education","lineage":["https://openalex.org/I72264486"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Meraj Ali Khan","raw_affiliation_strings":["Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia","institution_ids":["https://openalex.org/I72264486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034019750","display_name":"Aliya Naaz S\u0131dd\u0131qu\u0131","orcid":"https://orcid.org/0000-0003-3895-7548"},"institutions":[{"id":"https://openalex.org/I155125381","display_name":"Galgotias University","ror":"https://ror.org/02w8ba206","country_code":"IN","type":"education","lineage":["https://openalex.org/I155125381"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Aliya Naaz Siddiqui","raw_affiliation_strings":["Division of Mathematics, School of Basic & Applied Sciences, Galgotias University, Greater Noida, Uttar Pradesh 203201, India"],"affiliations":[{"raw_affiliation_string":"Division of Mathematics, School of Basic & Applied Sciences, Galgotias University, Greater Noida, Uttar Pradesh 203201, India","institution_ids":["https://openalex.org/I155125381"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5034019750"],"corresponding_institution_ids":["https://openalex.org/I155125381"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.4242,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.80323847,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"11","issue":"11","first_page":"594","last_page":"594"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9998999834060669,"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":0.9998999834060669,"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/T12351","display_name":"Geometry and complex manifolds","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9972000122070312,"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/mathematics","display_name":"Mathematics","score":0.6882114410400391},{"id":"https://openalex.org/keywords/conformal-map","display_name":"Conformal map","score":0.6378422975540161},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.6307977437973022},{"id":"https://openalex.org/keywords/riemannian-submersion","display_name":"Riemannian submersion","score":0.6083861589431763},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.5054857730865479},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.5022380352020264},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4872092604637146},{"id":"https://openalex.org/keywords/ricci-flat-manifold","display_name":"Ricci-flat manifold","score":0.48244863748550415},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.47146493196487427},{"id":"https://openalex.org/keywords/curvature-of-riemannian-manifolds","display_name":"Curvature of Riemannian manifolds","score":0.45637524127960205},{"id":"https://openalex.org/keywords/ricci-flow","display_name":"Ricci flow","score":0.45533910393714905},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.4504748284816742},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44621050357818604},{"id":"https://openalex.org/keywords/first-variation","display_name":"First variation","score":0.44324877858161926},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4178531765937805},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10489428043365479},{"id":"https://openalex.org/keywords/sectional-curvature","display_name":"Sectional curvature","score":0.06287312507629395}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6882114410400391},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.6378422975540161},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.6307977437973022},{"id":"https://openalex.org/C82978714","wikidata":"https://www.wikidata.org/wiki/Q4394657","display_name":"Riemannian submersion","level":5,"score":0.6083861589431763},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.5054857730865479},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5022380352020264},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4872092604637146},{"id":"https://openalex.org/C203934109","wikidata":"https://www.wikidata.org/wiki/Q7322952","display_name":"Ricci-flat manifold","level":4,"score":0.48244863748550415},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.47146493196487427},{"id":"https://openalex.org/C146674193","wikidata":"https://www.wikidata.org/wiki/Q40139","display_name":"Curvature of Riemannian manifolds","level":5,"score":0.45637524127960205},{"id":"https://openalex.org/C148729565","wikidata":"https://www.wikidata.org/wiki/Q1361396","display_name":"Ricci flow","level":4,"score":0.45533910393714905},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.4504748284816742},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44621050357818604},{"id":"https://openalex.org/C136005978","wikidata":"https://www.wikidata.org/wiki/Q1362077","display_name":"First variation","level":2,"score":0.44324877858161926},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4178531765937805},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10489428043365479},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.06287312507629395},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11110594","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110594","pdf_url":"https://www.mdpi.com/2075-1680/11/11/594/pdf?version=1669106079","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8a951de8f3324724bbc569de36aa1dbb","is_oa":true,"landing_page_url":"https://doaj.org/article/8a951de8f3324724bbc569de36aa1dbb","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 11, p 594 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/11/594/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11110594","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":"Axioms; Volume 11; Issue 11; Pages: 594","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11110594","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110594","pdf_url":"https://www.mdpi.com/2075-1680/11/11/594/pdf?version=1669106079","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1380584810","display_name":null,"funder_award_id":"R.G.P","funder_id":"https://openalex.org/F4320324433","funder_display_name":"King Khalid University"},{"id":"https://openalex.org/G8305986263","display_name":null,"funder_award_id":"R.G.P.2/199/43","funder_id":"https://openalex.org/F4320324433","funder_display_name":"King Khalid University"}],"funders":[{"id":"https://openalex.org/F4320324433","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4307633525.pdf","grobid_xml":"https://content.openalex.org/works/W4307633525.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1539008584","https://openalex.org/W1995864047","https://openalex.org/W2018216665","https://openalex.org/W2061781546","https://openalex.org/W2106743668","https://openalex.org/W2970690066","https://openalex.org/W2981676835","https://openalex.org/W3021918379","https://openalex.org/W3033605608","https://openalex.org/W3117949140","https://openalex.org/W3215854781","https://openalex.org/W4235304608","https://openalex.org/W4238350631","https://openalex.org/W4242771523","https://openalex.org/W4249250785","https://openalex.org/W4249279429","https://openalex.org/W4292184660","https://openalex.org/W4296020618","https://openalex.org/W4296052929","https://openalex.org/W4296284611","https://openalex.org/W4298004036","https://openalex.org/W4298848800","https://openalex.org/W6750619582","https://openalex.org/W6864272057"],"related_works":["https://openalex.org/W4367860315","https://openalex.org/W2963654695","https://openalex.org/W2096986877","https://openalex.org/W2963372221","https://openalex.org/W4285160888","https://openalex.org/W2950383185","https://openalex.org/W3177220932","https://openalex.org/W2003298539","https://openalex.org/W2521464350","https://openalex.org/W2166551806"],"abstract_inverted_index":{"This":[0],"research":[1],"article":[2],"endeavors":[3],"to":[4],"discuss":[5],"the":[6,12,18,36,41,48,68,76,86,95],"attributes":[7],"of":[8,17,44,85,98,127],"Riemannian":[9,45,73,128,131],"submersions":[10,129],"under":[11,47,75,101],"canonical":[13,49,77,102],"variation":[14,50,78,103],"in":[15],"terms":[16],"conformal":[19,24,53,110],"\u03b7-Ricci":[20,25,54,111],"soliton":[21,26,55,112],"and":[22,61,92],"gradient":[23,109],"with":[27,56,113],"a":[28,52,57,62,81,114],"potential":[29,88],"vector":[30,59,89],"field":[31,60,90,117],"\u03b6.":[32],"Additionally,":[33],"we":[34,66,123],"estimate":[35],"various":[37],"conditions":[38],"for":[39,72,108],"which":[40,133],"target":[42],"manifold":[43,97],"submersion":[46,74,100],"is":[51,104],"Killing":[58],"\u03c6(Ric)-vector":[63],"field.":[64],"Moreover,":[65],"deduce":[67],"generalized":[69],"Liouville":[70],"equation":[71],"satisfying":[79],"by":[80],"last":[82],"multiplier":[83],"\u03a8":[84],"vertical":[87],"\u03b6":[91],"show":[93],"that":[94],"base":[96,120],"Riemanian":[99],"an":[105,125],"\u03b7":[106],"Einstein":[107],"scalar":[115],"concircular":[116],"\u03b3":[118],"on":[119],"manifold.":[121],"Finally,":[122],"illustrate":[124],"example":[126],"between":[130],"manifolds,":[132],"verify":[134],"our":[135],"results.":[136]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2026-03-15T09:29:46.208133","created_date":"2022-11-04T00:00:00"}