Homogeneous isoparametric submanifolds of Hilbert space [Elektronische Ressource] / von Kerstin Weinl

Kerstin Weinl

Sujets

• Mathematics

Informations

• Publié par: universitat_augsburg
• Publié le: 01 janvier 2007
• Nombre de lectures: 21
• Langue: Deutsch

Extrait

WHomogeneousderisophenarametricAugsburgsubmanif06oldsakulofersitHilberontAugsburgsphaftlicaFceatInaugural-DissertationUnivzuratErlangungvdesKerstinDoktorgradeseinlder20Mathematisch-NaturwissenscErstgutacProf.hbtTer:Prof.teDr.CarlosErnstderHeinhentze13.Zw2006eitgutacr:hDr.ter:OlmosProf.agDr.mJost-HinricundlichPrEscufung:henDezemburgerDrittgutachDiagramsCon4.6.ten1tsofListDatenof4.4.T)-actionsables1,iv73In39troKduction4.5.1diagramsChapterane1.yAmRigiditey82Theoremedforthomogeneous42isopKarametrClassicalicExceptionalsubmanifoldsactions3P1.1.withPreliminaryChapterDenitions5.1.andUniformResults673Exclusion1.2.SomeReductionareofablesthePcoerdegangdimensionDynkin5Actions1.3.eNormalKhomogeneousGeometrystructures67-ActionsChapteron2.GroupsTheonisotropGroupsyyrepresen4.7.tationarisingofG;isoparametric4.8.hmarkypdiagramersurfacesRigidit10submanifolds2.1.mStructure63ofultiplicittheandprincipalNonisotrop69ysomegroup210on2.2.tations,Decomps-represenoendix.sitionBibliographofenslaufeigenspacesonlicE4niii14ane2.3.diagramsDecomp4.2.oofsitionypofKE=(0)2|4.3.assoofciated1mo=dules215452.4.ActionsMotheduLiele46sActionsofthetheLieisotrop50yCohomogeneitrepresenonetatio57nDynkinfornotirreduciblefromeigenspace(sHE59nActions17equal2.5.edReductionDynkinto60elemen5.taryyisoparametricisoparametrich62ypUniformersurfaceultiplicits2295.2.Chapterm3.yCanonical4connections8of5.3.isoparametricuniformhultiplicitiesyp5.4.ersurfacesof31DynkinChapter74.5.5.SliceremarksRepresenslictationsrepresenandthatDynnotkintationsDiagramsAppoTf76Py(LebG;84Hers)-Actionshe3884.1.WP84ossiblemarktationsListHermann-actionsof~TnablesActions2.1subactionsPt(onG;hHm)-actionultiplicitwithAne\exotic"MostprincipalAneisotrsingularodiagramspsubmanifoldsyygroupC135.32.2noExteOrbitnrepresensediLieontationsofLiemodiagramsdulesgroupsfromrepresenSO(groupsny)5.1toiSO(mn68+Diagram1)non21y4.1withP4ossibleuniformmark72edalenDynkinpdiagrams73forrhomogeneousdiagramsisoparametricthesubmanifolds77ofsliceHilbHermann-actionsertespa78cedeHermann-actions41exceptional4.2A.4DynkincdiagramsofofexceptionalA.5-actionsprincipal45of4.3ivMultiplicitieIsoparametricswoftactionsuniformarisingultiplicitfromonerank-25.2symmetricwithspaces~58and4.4uniformMultiplicitieultiplicits71ofActionsexceptionalDiagramactionsFonandsimnplemgroupsy585.44.5equivPt(ofG;olarHtations)-actionsA.1withmatheksameDynkinaneofmarkonedclassicalDynkingroupsdiagramA.2butsingulardierenrepresentofsingularonslicehrepresenclassicaltationgroupssA.361mark4.6DynkinPof(oG;theHLie)-actions79withMosttheslisameeanetationsmarkHermann-actionsedtheDynkinLiediagram80andDynkintheandsameisotropsingulargroupsslices-represenrepresen81tations61HilbInintroypductionspaces.Thespaceaimthanofcthisgrethesisofiseigenspacesto1proovede[rigiditricyHL99resultssuggestsforobtainhomogeneous(isoparametrictationsubmanifolds(oftheseHilbanertalreadyspace]..tAolarsubmanclassicationifoldhomogeneitMareofisaforspacetheformdimensionordyaofHilbisoeadditionalrtirreduciblespacesubmanifoldV2),is~c]).awithlledbisoparametricanifspace,itspronormalabundleo00ishandatonandsymmetrictheskprincipalprocurvKac-Moaturesdimensions,alongisopaparallelertnormalceldsthanaretzeconstannot.inhomogeneousTheasbtheeginningthoseofshouldtheofstudythisofforisoparametricsubmanifoldshvingypprincipalersurfacesEssedatesonbacekthetoincludes1920diagramandnthese,early;in~v([estigationsyculmiannateydmainseenthetationswKacorksymmet-ofobservthoughElieeCartanHPTT94in[the([1930s.proInthethes-represeearlyt1980sanetheonotionarewHeinashesgeneralized]fromforisoparametricahdyypinersurfacesistoresultsubmanifoldsaofofhigher|coifdimensiondimensioninteRThisntobLiuySoTresult,erngnor([submanifoldsTer85space,])wn,andtothers;dimensionalinatafsubsequenthantepappresenerKac-Moshespaces.furtherwgeneralizesythecertaindenitionisopara-toHilbsubmanifoldsyoftheyHilbricertofspaceH([tiallyTer89pt]).thatHomogeneoustheisoparametriceratorsubmanifoldsdulesareycloselyThisrelatedytoanepofolar~reprensenDta-Etions,=i.e.;re4presen2tationserngwhicTer95hManadmitofa(e.g.section,yacohomogeneitsubmanifolgreaterdone)thatyinetersectsasans-represenyoforbitanep-Moerpdyendicularlyric.anPationolarmadereprenotsenvtationsno[f]compactndLieTer95groupsGrossonGrR])nvwonereotherclas-thatsiednbayiDadokof([KaD-Moad85dy]).spacesTheypareandorbit-equivtzealenetctintoHei06s-represenatations,ofi.e.theiso-oftropneyorepresensymmetrictAsa