[美国数学本科生，研究生基础课程参考书目].9.-.riemannian.geometry.-.i.chavel

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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