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1、LecturesonClassicalDifferentialGeometrySECONDEDITIONDirkJ.StruikMASSACHUSETTSINSTITUTEOFTECHNOLOGYDOVERPUBLICATIONS,INC.NewYorkCopyright©1950,1961byDirkJ.Struik.AllrightsreservedunderPanAmericanandInternationalCopyrightConventions.PublishedinCanadabyGeneralPublishingCompany,Lt
2、d.,30LesmillRoad,DonMills,Toronto,Ontario.PublishedintheUnitedKingdombyConstableandCom-pany,Ltd.ThisDoveredition,firstpublishedin1988,isanun-abridgedandunalteredrepublicationofthesecondedition(1961)oftheworkfirstpublishedin1950bytheAddison-WesleyPublishingCompany,Inc.,Reading,
3、Massachusetts.ManufacturedintheUnitedStatesofAmericaDoverPublications,Inc.,31East2ndStreet,Mineola,N.Y.11501LibraryofCongressCataloging-in-PublicationDataStruik,DirkJan,1894-Lecturesonclassicaldifferentialgeometry/DirkJ.Struik.-2nded.p.cm.Reprint.Originallypublished:Reading,Ma
4、ss.:Addi-son-WesleyPub.Co.,1961.Bibliography:p.Includesindex.ISBN0-486-65609-81.Geometry,Differential.I.Title.QA641.S721988516.3'602-dc1987-34903CIPCONTENTSPREFACE.......................VBIBLIOGRAPHY.....................ViiCHAPTER1.CURVES..................11-1Analyticrepresent
5、ation...............11-2Arclength,tangent.................51-3Osculatingplane..................101-4Curvature....................131-5Torsion.....................151-6FormulasofFrenet.................181-7Contact.....................231-8Naturalequations.................261-9H
6、elices.....................331-10Generalsolutionofthenaturalequations.........361-11Evolutesandinvolutes................391-12Imaginarycurves.................441-13Ovals......................471-14Monge.....................53CHAPTER2.ELEMENTARYTHEORYOFSURFACES.......552-1Analy
7、ticalrepresentation...............552-2Firstfundamentalform...............582-3Normal,tangentplane................622-4Developablesurfaces................662-5Secondfundamentalform.Meusnier'stheorem.......732-6Euler'stheorem..................772-7Dupin'sindicatrix.............
8、....832-8Somesurfaces...................862-9Ageometricalinte
