{"id":"https://openalex.org/W7126245424","doi":"https://doi.org/10.3390/axioms15020103","title":"Geometry of Lightlike Hypersurfaces in a Class of Almost (\u03b1, p)-Metallic Semi-Riemannian Manifold","display_name":"Geometry of Lightlike Hypersurfaces in a Class of Almost (\u03b1, p)-Metallic Semi-Riemannian Manifold","publication_year":2026,"publication_date":"2026-01-30","ids":{"openalex":"https://openalex.org/W7126245424","doi":"https://doi.org/10.3390/axioms15020103"},"language":"en","primary_location":{"id":"doi:10.3390/axioms15020103","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15020103","pdf_url":"https://www.mdpi.com/2075-1680/15/2/103/pdf","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/2075-1680/15/2/103/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Rajinder Kaur","orcid":"https://orcid.org/0009-0002-2039-7167"},"institutions":[{"id":"https://openalex.org/I79161377","display_name":"Punjabi University","ror":"https://ror.org/00xdn8y92","country_code":"IN","type":"education","lineage":["https://openalex.org/I79161377"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Rajinder Kaur","raw_affiliation_strings":["Department of Mathematics, Punjabi University, Patiala 147002, Punjab, India"],"raw_orcid":"https://orcid.org/0009-0002-2039-7167","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Punjabi University, Patiala 147002, Punjab, India","institution_ids":["https://openalex.org/I79161377"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104149510","display_name":"V. G. Gupta","orcid":"https://orcid.org/0000-0003-2190-0174"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vandana Gupta","raw_affiliation_strings":["Department of Mathematics, Patel Memorial National College, Rajpura 140401, Punjab, India"],"raw_orcid":"https://orcid.org/0000-0003-2190-0174","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Patel Memorial National College, Rajpura 140401, Punjab, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103198603","display_name":"Jasleen Kaur","orcid":"https://orcid.org/0000-0002-4284-2842"},"institutions":[{"id":"https://openalex.org/I79161377","display_name":"Punjabi University","ror":"https://ror.org/00xdn8y92","country_code":"IN","type":"education","lineage":["https://openalex.org/I79161377"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Jasleen Kaur","raw_affiliation_strings":["Department of Mathematics, Punjabi University, Patiala 147002, Punjab, India"],"raw_orcid":"https://orcid.org/0000-0002-4284-2842","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Punjabi University, Patiala 147002, Punjab, India","institution_ids":["https://openalex.org/I79161377"]}]},{"author_position":"last","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":true,"raw_author_name":"Ibrahim Al-Dayel","raw_affiliation_strings":["Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMISU), Riyadh 11564, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-5901-2511","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMISU), Riyadh 11564, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5006916462"],"corresponding_institution_ids":["https://openalex.org/I240666556"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2229461,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"2","first_page":"103","last_page":"103"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9696000218391418,"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":0.9696000218391418,"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":0.00800000037997961,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.002199999988079071,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/hypersurface","display_name":"Hypersurface","score":0.8858000040054321},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6455000042915344},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6331999897956848},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.39640000462532043},{"id":"https://openalex.org/keywords/parallelism","display_name":"Parallelism (grammar)","score":0.33079999685287476},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.28929999470710754}],"concepts":[{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.8858000040054321},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6455000042915344},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6331999897956848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.585099995136261},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4941999912261963},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4896000027656555},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.39640000462532043},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33169999718666077},{"id":"https://openalex.org/C2781172179","wikidata":"https://www.wikidata.org/wiki/Q853109","display_name":"Parallelism (grammar)","level":2,"score":0.33079999685287476},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C158843486","wikidata":"https://www.wikidata.org/wiki/Q2137810","display_name":"Complex geometry","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C105653879","wikidata":"https://www.wikidata.org/wiki/Q7100712","display_name":"Ordered geometry","level":5,"score":0.2775999903678894}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms15020103","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15020103","pdf_url":"https://www.mdpi.com/2075-1680/15/2/103/pdf","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:89f0b8641740403f868fb1c2c5bdcd09","is_oa":false,"landing_page_url":"https://doaj.org/article/89f0b8641740403f868fb1c2c5bdcd09","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":"Axioms, Vol 15, Iss 2, p 103 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms15020103","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15020103","pdf_url":"https://www.mdpi.com/2075-1680/15/2/103/pdf","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/G7583256456","display_name":null,"funder_award_id":"IMSIU-DDRSP2602","funder_id":"https://openalex.org/F4320321420","funder_display_name":"Imam Mohammed Ibn Saud Islamic University"}],"funders":[{"id":"https://openalex.org/F4320321420","display_name":"Imam Mohammed Ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39"},{"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/W7126245424.pdf","grobid_xml":"https://content.openalex.org/works/W7126245424.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"aim":[1],"of":[2,10,23,42,64],"this":[3],"paper":[4],"is":[5],"to":[6],"investigate":[7],"the":[8,21,24,32,40,65],"geometry":[9,41],"lightlike":[11,29,48],"hypersurfaces":[12,49],"in":[13],"an":[14,51],"(\u03b1,p)-silver":[15,33,53],"semi-Riemannian":[16,34,54],"manifold.":[17,55],"Our":[18],"work":[19],"analyzes":[20],"behavior":[22],"structures":[25],"induced":[26],"on":[27],"a":[28],"hypersurface":[30],"by":[31],"framework.":[35],"We":[36],"define":[37],"and":[38,45,62,68],"introduce":[39],"invariant,":[43],"anti-invariant,":[44],"screen":[46],"semi-invariant":[47],"within":[50],"almost":[52],"Furthermore,":[56],"we":[57],"develop":[58],"results":[59],"concerning":[60],"parallelism":[61],"geodesicity":[63],"associated":[66],"distributions":[67],"illustrate":[69],"these":[70],"findings":[71],"with":[72],"suitable":[73],"examples.":[74]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2026-02-01T00:00:00"}