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ID:15289357
大小:3.01 MB
页数:489页
时间:2018-08-02
《[美国数学本科生,研究生基础课程参考书目].9.-.riemannian.geometry.-.i.chavel》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、P1:JZP052183774XpreCUNY374B/Angel052183774XApril9,20069:52P1:JZP0521853680preCB980/ChavelFebruary15,200611:6CharCount=0ThispageintentionallyleftblankiiP1:JZP0521853680preCB980/ChavelFebruary15,200611:6CharCount=0RIEMANNIANGEOMETRYAModernIntroductionSecondEditionThisbookprovidesanin
2、troductiontoRiemanniangeometry,thegeometryofcurvedspaces,foruseinagraduatecourse.Requiringonlyanunderstandingofdifferentiablemanifolds,thebookcoverstheintroductoryideasofRiemanniangeometry,followedbyaselectionofmorespecializedtopics.AlsofeaturedareNotesandExercisesforeachchaptertod
3、evelopandenrichthereader’sappreciationofthesubject.Thissecondeditionhasaclearertreatmentofmanytopicsfromthefirstedition,withnewproofsofsometheorems.AlsoanewchapterontheRiemanniangeometryofsurfaceshasbeenadded.ThemainthemesherearetheeffectofcurvatureontheusualnotionsofclassicalEuclid
4、eangeometry,andthenewnotionsandideasmotivatedbycur-vatureitself.Amongtheclassicaltopicsshowninanewsettingisisoperimetricinequalities–theinterplayofvolumeofsetsandtheareasoftheirbound-aries–incurvedspace.CompletelynewthemescreatedbycurvatureincludetheclassicalRauchcomparisontheorema
5、nditsconsequencesingeometryandtopology,andtheinteractionofmicroscopicbehaviorofthegeometrywiththemacroscopicstructureofthespace.IsaacChavelisProfessorofMathematicsatTheCityCollegeoftheCityUniversityofNewYork.HereceivedhisPh.D.inMathematicsfromYeshivaUniversityunderthedirectionofPro
6、fessorHarryE.Rauch.Hehaspublishedininternationaljournalsintheareasofdifferentialgeometryandpartialdifferen-tialequations,especiallytheLaplaceandheatoperatorsonRiemannianmani-folds.HisotherbooksincludeEigenvaluesinRiemannianGeometry(1984)andIsoperimetricInequalities:DifferentialGeom
7、etricandAnalyticPerspectives(2001).HehasbeenteachingatTheCityCollegeoftheCityUniversityofNewYorksince1970,andhehasbeenamemberofthedoctoralprogramoftheCityUniversityofNewYorksince1976.HeisamemberoftheAmericanMathematicalSociety.iP1:JZP0521853680preCB980/ChavelFebruary15,200611:6Char
8、Count=0iiP1:JZP0521853680p
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