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1、TensorAnalysisonManifoldsRichardL.BishopUniversityofIllinoisSamuelI.GoldbergUniversityofIllinoisBig"'_cmtraleFacjliaInyagneria0G0312DoverPublications,Inc.NewYorkCopyright©1968,1980byRichardLBishopandSamuelIGoldbergAllrightsreservedunderPanAmericanandInternationa
2、lCopyrightConventionsThisDoveredition,firstpublishedin1980,isanunabridg(andcorrectedrepublicationoftheworkoriginallypublishibyTheMacmillanCompanyin1968InternationalStandardBookNumber0-486-64039-6LibraryofCongressCatalogCardNumber80-66959ManufacturedintheUnitedSt
3、atesofAmericaDoverPublications,Inc31East2ndStreet,Mineola,N.Y.11501Preface"SiebedeuteteinenwahrenTriumphderdurchGauss,Riemann,Christoffel,Ricci...begrundetenMethodendesallgemeinenDifferentialcalculus."ALBERTEINSTEIN,1915SINCEITSDEVELOPMENTBYRiccibetween1887and18
4、96,tensoranalysishashadaratherrestrictedoutlookdespiteitsstrikingsuccessasamathematicaltoolinthegeneraltheoryofrelativityanditsadaptabilitytoawiderangeofproblemsindifferentialequations,geometry,andphysics.Theemphasishasbeenonnotationandmanipulationofindices.This
5、bookisanattempttobroadenthispointofviewatthestagewherethestudentfirstencountersthesubject.Wehavetreatedtensoranalysisasacontinuationofadvancedcalcu-lus,andourstandardsofrigorandlogicalcompletenesscomparefavorablywithparallelcoursesinthecurriculumsuchascomplexvar
6、iabletheoryandlinearalgebra.Forstudentsinthephysicalsciences,whoacquiremathematicalknowledgeona"need-to-know"basis,thisbookprovidesorganization.Ontheotherhand,itcanbeusedbymathematicsstudentsasameaningfulintroductiontodifferentialgeometry.Abroadrangeofnotationsi
7、sexplainedandinterrelated,sothestudentwillbeabletocontinuehisstudiesamongeithertheclassicalreferences,thoseinthestyleofE.Cartan,orthecurrentabstractions.Thematerialhasbeenorganizedaccordingtothedictatesofmathematicalstructure,proceedingfromthegeneraltothespecial
8、.Theinitialchapterhasbeennumbered0becauseitlogicallyprecedesthemaintopics.ThusChapter0establishesnotationandgivesanoutlineofabodyoftheoryrequiredtoputtheremainingchap
