{"id":"https://openalex.org/W7225626854","doi":"https://doi.org/10.5281/zenodo.24068623","title":"Prime geodesic periods on manifolds of complex projective type","display_name":"Prime geodesic periods on manifolds of complex projective type","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225626854","doi":"https://doi.org/10.5281/zenodo.24068623"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24068623","doi":"https://doi.org/10.5281/zenodo.24068623","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24068623","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24068623","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133211680","display_name":"Anass NIFA","orcid":"https://orcid.org/0000-0002-8986-7123","observed_orcids":["https://orcid.org/0000-0002-8986-7123"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nifa, Anass","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-8986-7123","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5133211680"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.48579999804496765,"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"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.48579999804496765,"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":0.21799999475479126,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.051899999380111694,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/closed-geodesics","display_name":"closed geodesics","score":0.8989999890327454},{"id":"https://openalex.org/keywords/circle-actions","display_name":"circle actions","score":0.5580000281333923},{"id":"https://openalex.org/keywords/geodesic-flow","display_name":"geodesic flow","score":0.6880000233650208},{"id":"https://openalex.org/keywords/critical-manifold","display_name":"critical manifold","score":0.7440000176429749},{"id":"https://openalex.org/keywords/betti-numbers","display_name":"Betti numbers","score":0.6499999761581421},{"id":"https://openalex.org/keywords/riemannian-manifolds","display_name":"Riemannian manifolds","score":0.828000009059906}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.847599983215332},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.7386999726295471},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5860999822616577},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5792999863624573},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.5001000165939331},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4871000051498413},{"id":"https://openalex.org/C53936288","wikidata":"https://www.wikidata.org/wiki/Q2634828","display_name":"Inverse limit","level":2,"score":0.41339999437332153},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.382099986076355},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3449000120162964},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.3407000005245209},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C156730297","wikidata":"https://www.wikidata.org/wiki/Q2296951","display_name":"Morse theory","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C129621563","wikidata":"https://www.wikidata.org/wiki/Q429593","display_name":"Betti number","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C162269530","wikidata":"https://www.wikidata.org/wiki/Q17100560","display_name":"Geodesic map","level":3,"score":0.3059000074863434},{"id":"https://openalex.org/C191403955","wikidata":"https://www.wikidata.org/wiki/Q526901","display_name":"3-manifold","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C2776730729","wikidata":"https://www.wikidata.org/wiki/Q1392130","display_name":"Flag (linear algebra)","level":3,"score":0.29660001397132874},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C74349738","wikidata":"https://www.wikidata.org/wiki/Q1517914","display_name":"Closed manifold","level":3,"score":0.28459998965263367},{"id":"https://openalex.org/C1432948","wikidata":"https://www.wikidata.org/wiki/Q5741935","display_name":"Hermitian manifold","level":4,"score":0.2825999855995178},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.27959999442100525},{"id":"https://openalex.org/C59831887","wikidata":"https://www.wikidata.org/wiki/Q7887158","display_name":"Unit tangent bundle","level":4,"score":0.26170000433921814},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2540000081062317},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.25270000100135803},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.24068623","doi":"https://doi.org/10.5281/zenodo.24068623","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24068623","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24068624","doi":"https://doi.org/10.5281/zenodo.24068624","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24068624","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24120100","doi":"https://doi.org/10.5281/zenodo.24120100","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24120100","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24068623","doi":"https://doi.org/10.5281/zenodo.24068623","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24068623","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1966672775","https://openalex.org/W1550905890","https://openalex.org/W7097508733","https://openalex.org/W2886031701","https://openalex.org/W1538559031","https://openalex.org/W2913470916","https://openalex.org/W2330250697","https://openalex.org/W2351093681","https://openalex.org/W1572461065","https://openalex.org/W7225004016"],"abstract_inverted_index":{"Let":[0],"M\u00b2\u207f,":[1],"n":[2,37,42,62],"\u2265":[3,43,63],"2,":[4,44],"be":[5],"a":[6,72,122],"closed":[7],"connected":[8,74],"Riemannian":[9],"manifold":[10,76],"all":[11,26],"of":[12,53,71,118,121],"whose":[13,77,90],"geodesics":[14,29],"are":[15],"closed,":[16],"and":[17,89,126,128],"assume":[18],"H\u00b2(M;":[19],"\u211a)":[20],"\u2260":[21],"0.":[22],"We":[23],"prove":[24],"that":[25],"prime":[27,66,87],"unit-speed":[28],"have":[30],"the":[31,45,54,69,116],"same":[32,46],"period":[33,107],"for":[34],"2":[35],"\u2264":[36,38],"8.":[39],"For":[40,61],"every":[41],"conclusion":[47],"holds":[48],"if":[49],"each":[50],"nontrivial":[51],"stabilizer":[52,79],"geodesic":[55,124],"circle":[56,96],"action":[57],"has":[58,81,98],"prime-power":[59],"order.":[60],"3,":[64],"unequal":[65],"periods":[67],"imply":[68],"existence":[70],"proper":[73],"critical":[75],"generic":[78],"order":[80],"at":[82,103],"least":[83,104],"two":[84],"distinct":[85],"odd":[86],"divisors":[88],"inverse":[91],"image":[92],"in":[93,112],"an":[94],"auxiliary":[95],"bundle":[97],"total":[99],"rational":[100],"Betti":[101],"number":[102],"eight.":[105],"The":[106],"restrictions":[108],"follow":[109],"from":[110],"reversal":[111],"equivariant":[113],"Morse":[114],"theory,":[115],"cohomology":[117],"fixed":[119],"manifolds":[120],"lifted":[123],"flow,":[125],"index":[127],"nullity":[129],"formulas":[130],"under":[131],"iteration.":[132]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}