{"id":"https://openalex.org/W2031136075","doi":"https://doi.org/10.1155/2014/398746","title":"Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn fontstyle=\"italic\">1</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">(</mml:mo><mml:mn fontstyle=\"italic\">1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:math>","display_name":"Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn fontstyle=\"italic\">1</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">(</mml:mo><mml:mn fontstyle=\"italic\">1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo></mml:math>","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2031136075","doi":"https://doi.org/10.1155/2014/398746","mag":"2031136075"},"language":"lv","primary_location":{"id":"doi:10.1155/2014/398746","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/398746","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2014/398746.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2014/398746.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100426706","display_name":"Junfeng Chen","orcid":"https://orcid.org/0000-0003-2486-2716"},"institutions":[{"id":"https://openalex.org/I4210118093","display_name":"Xianyang Normal University","ror":"https://ror.org/01r45yt97","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210118093"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junfeng Chen","raw_affiliation_strings":["School of Mathematics and Information Science, Xianyang Normal University, Xianyang, Shaanxi 712000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Xianyang Normal University, Xianyang, Shaanxi 712000, China","institution_ids":["https://openalex.org/I4210118093"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109105212","display_name":"\u0428\u0438\u0447\u0430\u043d\u0433 \u0428\u0443","orcid":null},"institutions":[{"id":"https://openalex.org/I4210118093","display_name":"Xianyang Normal University","ror":"https://ror.org/01r45yt97","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210118093"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shichang Shu","raw_affiliation_strings":["School of Mathematics and Information Science, Xianyang Normal University, Xianyang, Shaanxi 712000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Science, Xianyang Normal University, Xianyang, Shaanxi 712000, China","institution_ids":["https://openalex.org/I4210118093"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109105212"],"corresponding_institution_ids":["https://openalex.org/I4210118093"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13432096,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9965999722480774,"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":0.9965999722480774,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9897000193595886,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9865000247955322,"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/algorithm","display_name":"Algorithm","score":0.5712586641311646},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3577840030193329},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25960835814476013}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5712586641311646},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3577840030193329},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25960835814476013}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2014/398746","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/398746","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2014/398746.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8bc75c35886844da8fb1fe27509599aa","is_oa":true,"landing_page_url":"https://doaj.org/article/8bc75c35886844da8fb1fe27509599aa","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":"International Journal of Mathematics and Mathematical Sciences, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/398746","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/398746","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2014/398746.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2031136075.pdf","grobid_xml":"https://content.openalex.org/works/W2031136075.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1807164380","https://openalex.org/W1991688263","https://openalex.org/W1993436664","https://openalex.org/W1994839616","https://openalex.org/W2052307413","https://openalex.org/W2057848507","https://openalex.org/W2096842173","https://openalex.org/W2127960707","https://openalex.org/W2133164047","https://openalex.org/W2145160874","https://openalex.org/W2384806854","https://openalex.org/W2497406047"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2062023542"],"abstract_inverted_index":{"Let<mml:math":[0],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[1,9,29,37,40,53,61,66,77,81,97,112],"id=\"M2\"><mml:mi":[2],"mathvariant=\"bold\">x</mml:mi><mml:mo>:</mml:mo><mml:mi>M</mml:mi><mml:mo>\u21a6</mml:mo><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn":[3],"mathvariant=\"normal\">1</mml:mn></mml:mrow></mml:msup><mml:mo":[4,31,114],"stretchy=\"false\">(</mml:mo><mml:mn":[5,32,63,115],"mathvariant=\"normal\">1</mml:mn><mml:mo":[6,33,116],"stretchy=\"false\">)</mml:mo></mml:math>be":[7],"an<mml:math":[8],"id=\"M3\"><mml:mi>n":[10],"</mml:mi><mml:mo":[11],"stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>\u2265</mml:mo><mml:mn":[12],"mathvariant=\"normal\">3</mml:mn><mml:mo":[13],"stretchy=\"false\">)</mml:mo></mml:math>-dimensional":[14],"immersed":[15],"hypersurface":[16],"without":[17],"umbilical":[18],"points":[19],"and":[20,35,46],"with":[21],"vanishing":[22],"M\u00f6bius":[23,48],"form":[24,51],"in":[25],"a":[26,59,83,93],"unit":[27],"sphere<mml:math":[28],"id=\"M4\"><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn":[30],"stretchy=\"false\">)</mml:mo></mml:math>,":[34],"let<mml:math":[36],"id=\"M5\"><mml:mrow><mml:mi":[38],"mathvariant=\"bold\">A</mml:mi></mml:mrow></mml:math>and<mml:math":[39],"id=\"M6\"><mml:mrow><mml:mi":[41],"mathvariant=\"bold\">B</mml:mi></mml:mrow></mml:math>be":[42],"the":[43,47,73,88,108],"Blaschke":[44],"tensor":[45,75,90],"second":[49],"fundamental":[50],"of<mml:math":[52,76,96],"id=\"M7\"><mml:mrow><mml:mi":[54],"mathvariant=\"bold\">x</mml:mi></mml:mrow></mml:math>,":[55,79],"respectively.":[56],"We":[57],"define":[58],"symmetric<mml:math":[60],"id=\"M8\"><mml:mo":[62],"mathvariant=\"normal\">0,2</mml:mn><mml:mo":[64],"stretchy=\"false\">)</mml:mo></mml:math>tensor<mml:math":[65],"id=\"M9\"><mml:mi":[67],"mathvariant=\"bold\">D</mml:mi><mml:mo>=</mml:mo><mml:mi":[68],"mathvariant=\"bold\">A</mml:mi><mml:mo>+</mml:mo><mml:mi>\u03bb</mml:mi><mml:mi":[69],"mathvariant=\"bold\">B</mml:mi></mml:math>which":[70],"is":[71,91,105],"called":[72,92],"para-Blaschke":[74,89,94,120],"id=\"M10\"><mml:mrow><mml:mi":[78],"where<mml:math":[80],"id=\"M11\"><mml:mrow><mml:mi>\u03bb</mml:mi></mml:mrow></mml:math>is":[82],"constant.":[84],"An":[85],"eigenvalue":[86,95],"of":[87,102],"id=\"M12\"><mml:mrow><mml:mi":[98],"mathvariant=\"bold\">x</mml:mi></mml:mrow></mml:math>.":[99],"The":[100],"aim":[101],"this":[103],"paper":[104],"to":[106],"classify":[107],"oriented":[109],"hypersurfaces":[110],"in<mml:math":[111],"id=\"M13\"><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn":[113],"stretchy=\"false\">)</mml:mo></mml:math>with":[117],"two":[118],"distinct":[119],"eigenvalues":[121],"under":[122],"some":[123],"rigidity":[124],"conditions.":[125]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}