course of differential geometry - r. sharipov

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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.Thisbookisat

5、extbookforthebasiccourseofdierentialgeometry.Itisrecommendedasanintroductorymaterialforthissubject.InpreparingRussianeditionofthisbookIusedthecomputertypesettingonthebaseoftheAMS-TEXpackageandIusedCyrillicfontsoftheLh-familydistributedbytheCyrTUGassociationofCyrillic

6、TEXusers.EnglisheditionofthisbookisalsotypesetbymeansoftheAMS-TEXpackage.Referees:MathematicsgroupofUfaStateUniversityforAircraftandTechnology(UGATU);Prof.V.V.Sokolov,MathematicalInstituteofUralBranchofRussianAcademyofSciences(IMUrORAN).Contactstoauthor.Oce:Mathemati

7、csDepartment,BashkirStateUniversity,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:h

8、ttp://www.geocities.com/r-sharipovISBN5-7477-0129-0cSharipovR.A.,1996EnglishtranslationcSharipovR.A.,2004CONTENTS.CONTENTS................................................................................................3.PREFACE.........................................

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

10、...............6.x2.Thelengthintegralandthenaturalparametrizationofacurve..............10.x3.Frenetframe.ThedynamicsofFrenetframe.Curvatureandtorsionofaspacialcurve................................................................................12.x4.Thecurvaturecenter

11、andthecurvatureradiusofaspacialcurve.Theevoluteandtheevolventofacurve................................................14.x5.C