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1、DiracOperatorsinRiemannianGeometryThomasFriedrichGraduateStudiesinMathematicsVolume25AmericanMathematicalSocietyDiracOperatorsinRiemannianGeometryDiracOperatorsinRiemannianGeometryThomasFriedrichTranslatedbyAndreasNestkeGraduateStudiesinMathematicsVolum
2、e25AmericanMathematicalSocietyProvidence,RhodeIslandEditorialBoardHumphreys(Chair)DavidSaltmanDavidSattingerRonaldStern2000MathematicsSubjectClassification.Primary58Jxx;Secondary53C27,53C28,57R57,58J05,58J20,58J50,81R25.OriginallypublishedintheGermanlan
3、guagebyFriedr.Vieweg&SohnVerlagsge-sellschaftmbH,D-65189Wiesbaden,Germany,as"ThomasFriedrich:Dirac-OperatoreninderRiemannschenGeometrie.1.Auflage(1stedition)"©byFriedr.Vieweg&SohnVerlagsgesellschaftmbH,Braunschweig/Wiesbaden,1997TranslatedfromtheGermanb
4、yAndreasNestkeABSTRACT.ThistextexaminestheDiracoperatoronRiemannianmanifolds,especiallyitscon-nectionwiththeunderlyinggeometryandtopologyofthemanifold.Thepresentationincludesareviewofpreliminarymaterial,includingspinandspin0structures.Animportantlinkbet
5、weenthegeometryandtheanalysisisprovidedbyestimatesfortheeigenvaluesoftheDiracoperatorintermsofthescalarcurvatureandthesectionalcurvature.ConsiderationsofKillingspinorsandsolutionsofthetwistorequationonMleadtoresultsaboutwhetherMisanEinsteinmanifoldorcon
6、formallyequivalenttoone.AnappendixcontainsaconciseintroductiontotheSeiberg-Witteninvariants,whichareapowerfultoolforthestudyoffour-manifolds.Thisbookissuitableasatextforcoursesinadvanceddifferentialgeometryandglobalanalysis,andcanserveasanintroductionfo
7、rfurtherstudyintheseareas.LibraryofCongressCataloging-in-PublicationDataFriedrich,Thomas,1949-[Dirac-OperatoreninderRiemannschenGeometrie.English]DiracoperatorsinRiemanniangeometry/ThomasFriedrich;translatedbyAndreasNestke.p.cm.-(Graduatestudiesinmathem
8、atics,ISSN1065-7339;v.25)Includesbibliographicalreferencesandindex.ISBN0-8218-2055-9(alk.paper)1.Geometry,Riemannian.2.Diracequation.I.Title.II.Series.QA649.F685132000516.3'73-dc2l00-038614Copyingandreprinting.Individualreadersof
