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1、CURVATUREANDRevisedEditionSamuelI.GoldbergCURVATUREANDHOMOLOGYRevisedEditionSamuelI.GoldbergMathematiciansinterestedinthecurvaturepropertiesofRiemannianmani-foldsandtheirhomologicstructures,anincreasinglyimportantandspecializedbranchofdifferentialgeometry,willwelcomethisexcellentteachingtext.Revi
2、sedandexpandedbyitswell-knownauthor,thisvolumeoffersasystematicandself-containedtreatmentofsubjectssuchasthetopol-ogyofdifferentiatemanifolds,curvatureandhomologyofRiemannianman-ifolds,compactLiegroups,complexmanifolds,andthecurvatureandhomologyofKaehlermanifolds.Inadditiontoanewpreface,thisediti
3、onincludesfivenewappendicescon-cerningholomorphicbisectionalcurvature,theGauss-Bonnettheorem,someapplicationsofthegeneralizedGauss-Bonnettheorem,anapplicationofBochnerslemma,andtheKodairavanishingtheorems.Gearedtowardreadersfamiliarwithstandardcoursesinlinearalgebra,realandcomplexvariables,differ
4、entialequations,andpoint-settopology,thebookfeatureshelpfulexer-cisesattheendofeachchapterthatsupplementandclarifythetext.Thislucidandthoroughtreatment—hailedbyNaturemagazineas"...avaluablesurveyofrecentworkandofprobablelinesoffutureprogress"—includesmaterialunavailableelsewhereandprovidesanexcel
5、lentresourceforbothstudentsandteachers.UnabridgedDover(1998)correctedrepublicationoftheworkoriginallypub-lishedbyAcademicPress,NewYork,1962.NewPreface.Introduction.Fivenewappendixes.Bibliography.Indices.416pp.53/8x81/2Paperbound.FreeDoverMathematicsandScienceCatalog(59065-8)availableuponrequest.C
6、urvatureandHomologySAMUELI.GOLDBERGDepartmentofMathematicsUniversityofIllinois,Urbana-ChampaignDOVERPUBLICATIONS,INC.Mineola,NewYorkTomyparentsandmywifeCopyrightCopyright81962,1982,1998bySamuelI.GoldbergAllrightsreservedunderPanAmericanandInternationalCopyrightConventionsPublishedinCanadabyGenera
7、lPublishingCompany,Ltd.,30LesmillRoad,DonMills,Toronto,Ontario.PublishedintheUnitedKingdombyConstableandCompany,Ltd.,3TheLanchesters,162-164FulhamPalaceRoad,LondonW69ER.BibliographicalNoteThisDoverenlargededition,first
