course of differential geometry

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1、RUSSIANFEDERALCOMMITTEEFORHIGHEREDUCATIONBASHKIRSTATEUNIVERSITYSHARIPOVR.A.COURSEOFDIFFERENTIALGEOMETRYTheTextbookUfa19962MSC97U20UDC514.7SharipovR.A.CourseofDierentialGeometry:thetextbook/Publ.ofBashkirStateUniversity

2、Ufa,1996.

3、pp.132.

4、ISBN5-7477-0129-0.Thisbookisatextboo

5、kforthebasiccourseofdierentialgeometry.Itisrecommendedasanintroductorymaterialforthissubject.InpreparingRussianeditionofthisbookIusedthecomputertypesettingonthebaseoftheAMS-TEXpackageandIusedCyrillicfontsoftheLh-familydistributedbytheCyrTUGassociationofCyrillicTEXusers.Eng

6、lisheditionofthisbookisalsotypesetbymeansoftheAMS-TEXpackage.Referees:MathematicsgroupofUfaStateUniversityforAircraftandTechnology(UGATU);Prof.V.V.Sokolov,MathematicalInstituteofUralBranchofRussianAcademyofSciences(IMUrORAN).Contactstoauthor.Oce:MathematicsDepartment,Bashk

7、irStateUniversity,32Frunzestreet,450074Ufa,RussiaPhone:7-(3472)-23-67-18Fax:7-(3472)-23-67-74Home:5Rabochayastreet,450003Ufa,RussiaPhone:7-(917)-75-55-786E-mails:RSharipov@ic.bashedu.rur-sharipov@mail.rurasharipov@lycos.comrasharipov@hotmail.comURL:http://www.geocities.com/

8、r-sharipovISBN5-7477-0129-0cSharipovR.A.,1996EnglishtranslationcSharipovR.A.,2004CONTENTS.CONTENTS................................................................................................3.PREFACE.......................................................................

9、............................5.CHAPTERI.CURVESINTHREE-DIMENSIONALSPACE........................6.x1.Curves.Methodsofdeningacurve.Regularandsingularpointsofacurve.............................................................................................6.x2.Thelengthintegra

10、landthenaturalparametrizationofacurve..............10.x3.Frenetframe.ThedynamicsofFrenetframe.Curvatureandtorsionofaspacialcurve................................................................................12.x4.Thecurvaturecenterandthecurvatureradiusofaspacialcurve.Theev

11、oluteandtheevolventofacurve................................................14.x5.C