{"id":"https://openalex.org/W7225694226","doi":"https://doi.org/10.5281/zenodo.24101969","title":"Conformal natural rescalings of Riemannian metrics and isometric embeddings of submanifolds: an obstruction from the Weyl tensor","display_name":"Conformal natural rescalings of Riemannian metrics and isometric embeddings of submanifolds: an obstruction from the Weyl tensor","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225694226","doi":"https://doi.org/10.5281/zenodo.24101969"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24101969","doi":"https://doi.org/10.5281/zenodo.24101969","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24101969","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.24101969","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133245909","display_name":"Fumio Miyata","orcid":"https://orcid.org/0009-0008-8797-5578","observed_orcids":["https://orcid.org/0009-0008-8797-5578"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Miyata, Fumio","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0008-8797-5578","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5133245909"],"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9634000062942505,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9634000062942505,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.03460000082850456,"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":0.0005000000237487257,"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/weyl-tensor","display_name":"Weyl tensor","score":0.8700000047683716},{"id":"https://openalex.org/keywords/isometric-embedding","display_name":"isometric embedding","score":0.9150000214576721},{"id":"https://openalex.org/keywords/submanifolds","display_name":"submanifolds","score":0.9120000004768372},{"id":"https://openalex.org/keywords/riemannian-metrics","display_name":"Riemannian metrics","score":0.8019999861717224},{"id":"https://openalex.org/keywords/second-fundamental-form","display_name":"second fundamental form","score":0.6570000052452087},{"id":"https://openalex.org/keywords/gauss-equation","display_name":"Gauss equation","score":0.7680000066757202},{"id":"https://openalex.org/keywords/endofunctors","display_name":"endofunctors","score":0.6039999723434448},{"id":"https://openalex.org/keywords/automorphism-groups","display_name":"automorphism groups","score":0.7710000276565552},{"id":"https://openalex.org/keywords/conformal-geometry","display_name":"conformal geometry","score":0.367000013589859},{"id":"https://openalex.org/keywords/submanifold-geometry","display_name":"submanifold geometry","score":0.6150000095367432}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8519999980926514},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5940999984741211},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.574999988079071},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.5159000158309937},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.48260000348091125},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.47839999198913574},{"id":"https://openalex.org/C119830904","wikidata":"https://www.wikidata.org/wiki/Q233220","display_name":"Second fundamental form","level":4,"score":0.44600000977516174},{"id":"https://openalex.org/C183517385","wikidata":"https://www.wikidata.org/wiki/Q855112","display_name":"Riemann curvature tensor","level":3,"score":0.44179999828338623},{"id":"https://openalex.org/C91586840","wikidata":"https://www.wikidata.org/wiki/Q781415","display_name":"Volume form","level":5,"score":0.42149999737739563},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.40610000491142273},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.400299996137619},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.37630000710487366},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.36640000343322754},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.36340001225471497},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.36320000886917114},{"id":"https://openalex.org/C2777680557","wikidata":"https://www.wikidata.org/wiki/Q7259417","display_name":"Pullback","level":2,"score":0.3434000015258789},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.3319999873638153},{"id":"https://openalex.org/C198959055","wikidata":"https://www.wikidata.org/wiki/Q869108","display_name":"Weyl tensor","level":4,"score":0.3255999982357025},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.31940001249313354},{"id":"https://openalex.org/C103486182","wikidata":"https://www.wikidata.org/wiki/Q1216236","display_name":"Isometric exercise","level":2,"score":0.3176000118255615},{"id":"https://openalex.org/C125669323","wikidata":"https://www.wikidata.org/wiki/Q513175","display_name":"Conformal geometry","level":4,"score":0.3172000050544739},{"id":"https://openalex.org/C53216431","wikidata":"https://www.wikidata.org/wiki/Q3997736","display_name":"Weyl transformation","level":4,"score":0.30320000648498535},{"id":"https://openalex.org/C2779668893","wikidata":"https://www.wikidata.org/wiki/Q2250422","display_name":"Constant curvature","level":3,"score":0.30300000309944153},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C74349738","wikidata":"https://www.wikidata.org/wiki/Q1517914","display_name":"Closed manifold","level":3,"score":0.290800005197525},{"id":"https://openalex.org/C4306028","wikidata":"https://www.wikidata.org/wiki/Q2185349","display_name":"Fundamental theorem of Riemannian geometry","level":4,"score":0.27230000495910645},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C16140857","wikidata":"https://www.wikidata.org/wiki/Q945953","display_name":"Gaussian curvature","level":3,"score":0.27090001106262207},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.2689000070095062},{"id":"https://openalex.org/C14196021","wikidata":"https://www.wikidata.org/wiki/Q7240881","display_name":"Prescribed scalar curvature problem","level":5,"score":0.26660001277923584},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C3352285","wikidata":"https://www.wikidata.org/wiki/Q5422297","display_name":"Extremal length","level":4,"score":0.26339998841285706},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.25200000405311584},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.25110000371932983},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.250900000333786},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.25}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24101969","doi":"https://doi.org/10.5281/zenodo.24101969","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24101969","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.24101970","doi":"https://doi.org/10.5281/zenodo.24101970","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24101970","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.24101969","doi":"https://doi.org/10.5281/zenodo.24101969","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24101969","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/W7224087366","https://openalex.org/W4302309606","https://openalex.org/W2737300623","https://openalex.org/W2033674238","https://openalex.org/W2067701462","https://openalex.org/W6990025311","https://openalex.org/W568651912","https://openalex.org/W2009271817","https://openalex.org/W2028248565","https://openalex.org/W1568473583"],"abstract_inverted_index":{"We":[0,82,332],"consider":[1],"the":[2,22,46,107,110,115,131,134,150,154,176,206,214,219,281,313,324,339,366],"category":[3],"$\\mathrm{Riem}_n$":[4,18],"of":[5,17,45,72,78,80,87,106,114,123,136,142,157,178,180,213,218,236,254,280,284,338,353,365],"connected":[6],"Riemannian":[7,163,193],"$n$-manifolds":[8],"with":[9,97,167,232],"open":[10],"isometric":[11,89,140,190,234,308],"embeddings":[12,141,191,235,309,352],"as":[13,21,92,295],"morphisms,":[14],"and":[15,26,29,61,149,240,250,327],"endofunctors":[16],"that":[19,122,158,175,287,335],"act":[20],"identity":[23],"on":[24,153,246],"manifolds":[25,293],"smooth":[27,41],"maps":[28],"replace":[30],"each":[31],"metric":[32],"by":[33,121,130],"another":[34],"one.":[35],"For":[36,262,305,318],"$n":[37,168],"\\ge":[38,171],"4$,":[39],"every":[40],"positive":[42],"function":[43],"$f$":[44,243,328],"squared":[47,111,215],"Weyl":[48,112,216],"norm":[49,113,217],"$I_g":[50],"=":[51,59,169,264,273,289,299],"|W_g|^2$":[52],"defines":[53],"a":[54,70,103,143,161,183,196],"conformal":[55,336],"natural":[56],"rescaling":[57],"$\\Phi_f(g)":[58],"f(I_g)g$,":[60],"those":[62],"for":[63,84,160,291,301],"which":[64,85,127],"$t":[65],"\\mapsto":[66],"t":[67],"f(t)^{-2}$":[68],"is":[69,118,128,195,205,230,244,315],"diffeomorphism":[71],"$[0,\\infty)$":[73],"form":[74,340],"an":[75,251],"infinite-dimensional":[76,252],"group":[77],"automorphisms":[79,255],"$\\mathrm{Riem}_n$.":[81],"ask":[83],"classes":[86],"lower-dimensional":[88],"embeddings,":[90,346],"adjoined":[91],"morphisms":[93],"to":[94,101,343,348,361],"$\\mathrm{Riem}_n$,":[95],"compatibility":[96],"pullback":[98],"forces":[99],"$\\Phi_f$":[100,229],"be":[102,330,362],"constant":[104,245,363],"multiple":[105],"metric.":[108,367],"Because":[109],"ambient":[116],"curvature":[117,221],"bounded":[119,147],"below":[120],"its":[124],"tangential":[125,220],"part,":[126],"determined":[129],"Gauss":[132],"equation,":[133],"values":[135,179],"$I_g$":[137,181],"attainable":[138],"along":[139],"single":[144],"manifold":[145,164],"are":[146,359],"below,":[148],"answer":[151],"depends":[152],"intrinsic":[155],"geometry":[156],"manifold:":[159],"fixed":[162],"$(\\Sigma^m,":[165],"h)$":[166,238],"m+1":[170],"5$":[172],"we":[173,266],"show":[174,334],"set":[177],"at":[182],"point":[184],"$p":[185],"\\in":[186],"\\Sigma$,":[187],"over":[188,208],"all":[189,233,344,349],"into":[192],"$n$-manifolds,":[194],"half-line":[197],"$[c(p),":[198],"\\infty)$":[199],"(or":[200],"$(c(p),":[201],"\\infty)$),":[202],"where":[203],"$c(p)$":[204],"infimum":[207],"second":[209],"fundamental":[210],"forms":[211],"$k$":[212],"$R^h_p":[222],"-":[223,276],"\\tfrac12":[224],"k":[225],"\\owedge":[226],"k$.":[227],"Consequently,":[228],"compatible":[231],"$(\\Sigma,":[237],"if":[239,242],"only":[241],"$[\\inf_p":[247],"c(p),":[248],"\\infty)$,":[249],"subgroup":[253],"survives":[256],"whenever":[257],"$\\inf_p":[258,316],"c(p)":[259],">":[260],"0$.":[261],"$m":[263],"4$":[265],"compute":[267],"$c$":[268],"in":[269,278,310,321],"closed":[270],"form,":[271],"$c":[272,288,298],"2\\sum_i":[274],"(w_i^+":[275],"w_i^-)^2$":[277],"terms":[279],"ordered":[282],"eigenvalues":[283],"$W^\\pm$,":[285],"so":[286],"|W|^2/2$":[290],"half-conformally-flat":[292],"such":[294],"$\\mathbb{CP}^2$,":[296],"whereas":[297],"0$":[300],"$S^2":[302],"\\times":[303],"S^2$.":[304],"totally":[306,350],"geodesic":[307,351],"any":[311,354],"codimension":[312],"threshold":[314,325],"|W^h_p|^2$.":[317],"three-dimensional":[319],"hypersurfaces":[320],"dimension":[322,355],"four":[323],"vanishes":[326],"must":[329],"constant.":[331],"also":[333],"rescalings":[337],"$f(\\mathrm{Scal}_g)\\,g$":[341],"extending":[342],"hypersurface":[345],"or":[347],"$1\\le":[356],"m\\le":[357],"n-1$,":[358],"forced":[360],"multiples":[364],"code:":[368],"MIT,":[369],"manuscript/documentation:":[370],"CC":[371],"BY":[372],"4.0":[373]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-11T00:00:00"}