9.-.riemannian.geometry.-.i.chavel

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1、P1:JZP052183774XpreCUNY374B/Angel052183774XApril9,20069:52P1:JZP0521853680preCB980/ChavelFebruary15,200611:6CharCount=0ThispageintentionallyleftblankiiP1:JZP0521853680preCB980/ChavelFebruary15,200611:6CharCount=0RIEMANNIANGEOMETRYAModernIntroductionSecondEditionThisbookprovidesanintroductiontoR

2、iemanniangeometry,thegeometryofcurvedspaces,foruseinagraduatecourse.Requiringonlyanunderstandingofdifferentiablemanifolds,thebookcoverstheintroductoryideasofRiemanniangeometry,followedbyaselectionofmorespecializedtopics.AlsofeaturedareNotesandExercisesforeachchaptertodevelopandenrichthereader’s

3、appreciationofthesubject.Thissecondeditionhasaclearertreatmentofmanytopicsfromthefirstedition,withnewproofsofsometheorems.AlsoanewchapterontheRiemanniangeometryofsurfaceshasbeenadded.ThemainthemesherearetheeffectofcurvatureontheusualnotionsofclassicalEuclideangeometry,andthenewnotionsandideasmot

4、ivatedbycur-vatureitself.Amongtheclassicaltopicsshowninanewsettingisisoperimetricinequalities–theinterplayofvolumeofsetsandtheareasoftheirbound-aries–incurvedspace.CompletelynewthemescreatedbycurvatureincludetheclassicalRauchcomparisontheoremanditsconsequencesingeometryandtopology,andtheinterac

5、tionofmicroscopicbehaviorofthegeometrywiththemacroscopicstructureofthespace.IsaacChavelisProfessorofMathematicsatTheCityCollegeoftheCityUniversityofNewYork.HereceivedhisPh.D.inMathematicsfromYeshivaUniversityunderthedirectionofProfessorHarryE.Rauch.Hehaspublishedininternationaljournalsinthearea

6、sofdifferentialgeometryandpartialdifferen-tialequations,especiallytheLaplaceandheatoperatorsonRiemannianmani-folds.HisotherbooksincludeEigenvaluesinRiemannianGeometry(1984)andIsoperimetricInequalities:DifferentialGeometricandAnalyticPerspectives(2001).HehasbeenteachingatTheCityCollegeoftheCityU

7、niversityofNewYorksince1970,andhehasbeenamemberofthedoctoralprogramoftheCityUniversityofNewYorksince1976.HeisamemberoftheAmericanMathematicalSociety.iP1:JZP0521853680preCB980/ChavelFebruary15,200611:6CharCount=0iiP1:JZP0521853680p