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1、ApplieddifferentialgeometryWILLIAML.BURKEUniversityofCalifornia,SantaCruzghtoftheofCambridgetandsellerofbooks;1;1t°X311;antedby/11in1534.ityhasprinte4IIIk;:dcontinuousle1584.CAMBRIDGEUNIVERSITYPRESSCambridgeNewYorkNewRochelleMelbourneSydneyPublishedbythePressSyndicateoftheUniversityofCambridge
2、ThePittBuilding,TrumpingtonStreet,CambridgeCB21RP32East57thStreet,NewYork,NY10022,USA10StamfordRoad,Oakleigh,Melbourne3166,Australia@CambridgeUniversityPress1985Firstpublished1985EA.Reprinted1987(twice)PrintedintheUnitedStatesofAmericaLibraryofCongressCataloginginPublicationDataBurke,WilliamL.
3、Applieddifferentialgeometry.Bibliography:p.1.Geometry,Differential.2.Mathematicalphysics.1.Title.QC20.7.D52B871985516.3'684-14952ISBN0521263174hardcoversQ..ISBN0521269296paperbackToallthosewho,likeme,havewonderedhowinhellyoucanchange4withoutchangingq.ContentsPrefacepagexiGlossaryofnotationxvIn
4、troduction1ITensorsinlinearspaces111Linearandaffinespaces122Differentialcalculus213Tensoralgebra27--l4Alternatingproducts315Specialrelativity37--l6Theusesofcovariance44'''IIManifolds517Manifolds528Tangentvectorsand1-forms599Liebracket6810Tensorsonmanifolds72--+11Mappings7712Cotangentbundle8413
5、Tangentbundle9014Vectorfieldsanddynamicalsystems9415Contactbundles9916Thegeometryofthermodynamics108IIITransformations11517Liegroups11518Liederivative12119Holonomy132viiviiiContents20Contacttransformations13621Symmetries141IVThecalculusofdifferentialforms147F-.+22Differentialforms147.--23Exter
6、iorcalculus15324The*operator15925Metricsymmetries16926Normalforms17327Indexnotation17628Twisteddifferentialforms18329.o00Integration194-..-30Cohomology202VApplicationsoftheexteriorcalculus20731Diffusionequations207--+32First-orderpartialdifferentialequations21333Conservationlaws21934Calculusof
7、variations22535Constrainedvariations23336Variationsofmultipleintegrals23937Holonomyandthermodynamics24538Exteriordifferentialsystems248?39Symmetriesandsimilaritysolutions25840Variationalprinciplesandconservationlaws26441Whennottouseform
