{"id":"https://openalex.org/W4385812545","doi":"https://doi.org/10.3390/axioms12080784","title":"Finsler Warped Product Metrics with Special Curvature Properties","display_name":"Finsler Warped Product Metrics with Special Curvature Properties","publication_year":2023,"publication_date":"2023-08-12","ids":{"openalex":"https://openalex.org/W4385812545","doi":"https://doi.org/10.3390/axioms12080784"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12080784","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12080784","pdf_url":"https://www.mdpi.com/2075-1680/12/8/784/pdf?version=1692005616","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/2075-1680/12/8/784/pdf?version=1692005616","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103737064","display_name":"Lingen Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lingen Sun","raw_affiliation_strings":["College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100385986","display_name":"Xiaoling Zhang","orcid":"https://orcid.org/0000-0002-6369-9424"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaoling Zhang","raw_affiliation_strings":["College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109455321","display_name":"Mengke Wu","orcid":"https://orcid.org/0000-0002-7680-9055"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mengke Wu","raw_affiliation_strings":["College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China","institution_ids":["https://openalex.org/I96908189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100385986"],"corresponding_institution_ids":["https://openalex.org/I96908189"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.1766,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58197293,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"12","issue":"8","first_page":"784","last_page":"784"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":1.0,"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/curvature","display_name":"Curvature","score":0.8478660583496094},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6407796144485474},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5901728868484497},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5711138248443604},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.49454542994499207},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.48589056730270386},{"id":"https://openalex.org/keywords/finsler-manifold","display_name":"Finsler manifold","score":0.47599589824676514},{"id":"https://openalex.org/keywords/general-relativity","display_name":"General relativity","score":0.4727169871330261},{"id":"https://openalex.org/keywords/product-topology","display_name":"Product topology","score":0.44923171401023865},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4196837246417999},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39129623770713806},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"Scalar curvature","score":0.3731958568096161},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2334100306034088},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.11138495802879333},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10776206851005554},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.04304584860801697}],"concepts":[{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.8478660583496094},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6407796144485474},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5901728868484497},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5711138248443604},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.49454542994499207},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.48589056730270386},{"id":"https://openalex.org/C169316501","wikidata":"https://www.wikidata.org/wiki/Q2498782","display_name":"Finsler manifold","level":4,"score":0.47599589824676514},{"id":"https://openalex.org/C147452769","wikidata":"https://www.wikidata.org/wiki/Q11452","display_name":"General relativity","level":2,"score":0.4727169871330261},{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.44923171401023865},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4196837246417999},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39129623770713806},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.3731958568096161},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2334100306034088},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.11138495802879333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10776206851005554},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.04304584860801697},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12080784","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12080784","pdf_url":"https://www.mdpi.com/2075-1680/12/8/784/pdf?version=1692005616","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:93ae03a5d0644bf195950db83a9f9f0a","is_oa":true,"landing_page_url":"https://doaj.org/article/93ae03a5d0644bf195950db83a9f9f0a","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 12, Iss 8, p 784 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/8/784/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12080784","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 12; Issue 8; Pages: 784","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12080784","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12080784","pdf_url":"https://www.mdpi.com/2075-1680/12/8/784/pdf?version=1692005616","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/G3214160367","display_name":null,"funder_award_id":"No. 11","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5155884038","display_name":null,"funder_award_id":"11461064","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5167091242","display_name":null,"funder_award_id":"No. 1","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5174886991","display_name":null,"funder_award_id":"11961061","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6137401532","display_name":null,"funder_award_id":"No. 11961","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385812545.pdf","grobid_xml":"https://content.openalex.org/works/W4385812545.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W165894190","https://openalex.org/W1971507018","https://openalex.org/W1998326705","https://openalex.org/W2019280282","https://openalex.org/W2022228786","https://openalex.org/W2047935216","https://openalex.org/W2062346296","https://openalex.org/W2103337796","https://openalex.org/W2186155466","https://openalex.org/W2892999506","https://openalex.org/W3033228470","https://openalex.org/W3160667420","https://openalex.org/W3169756696","https://openalex.org/W6686656313","https://openalex.org/W6794963239","https://openalex.org/W6997299767"],"related_works":["https://openalex.org/W2011951582","https://openalex.org/W4282047881","https://openalex.org/W1994058842","https://openalex.org/W2949288431","https://openalex.org/W3006399673","https://openalex.org/W2170476843","https://openalex.org/W2889589649","https://openalex.org/W2019361733","https://openalex.org/W2947622417","https://openalex.org/W2066667131"],"abstract_inverted_index":{"The":[0],"class":[1],"of":[2,18,22,47,56],"warped":[3,58,73],"product":[4,59,74],"metrics":[5,60],"can":[6],"often":[7],"be":[8],"interpreted":[9],"as":[10],"key":[11],"space":[12],"models":[13],"for":[14,71],"the":[15,44,76,83],"general":[16],"theory":[17,21],"relativity":[19],"and":[20,80],"space\u2013time.":[23],"In":[24,50],"this":[25],"paper,":[26],"we":[27,52,68],"study":[28],"several":[29],"non-Riemannian":[30,36],"quantities":[31,37],"in":[32,42],"Finsler":[33,48,57,72],"geometry.":[34],"These":[35],"play":[38],"an":[39],"important":[40],"role":[41],"understanding":[43],"geometric":[45],"properties":[46],"metrics.":[49],"particular,":[51],"find":[53],"differential":[54],"equations":[55],"with":[61],"vanishing":[62,65],"\u03c7-curvature":[63,77],"or":[64],"H-curvature.":[66],"Furthermore,":[67],"show":[69],"that,":[70],"metrics,":[75],"vanishes":[78],"if":[79,82],"only":[81],"H-curvature":[84],"vanishes.":[85]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}