[黎曼几何].jost.riemannian.geometry.and.geome

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1、UniversitextJürgenJostRiemannianGeometryandGeometricAnalysisFourthEditionWith14Figures123JürgenJostMaxPlanckInstituteforMathematicsintheSciencesInselstr.2204103LeipzigGermanye-mail:jost@mis.mpg.deMathematicsSubjectClassification(2000):53B21,53L20,32C17,35I60,49-XX,58

2、E20,57R15LibraryofCongressControlNumber:2005925885ISBN-103-540-25907-4SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-25907-7SpringerBerlinHeidelbergNewYorkISBN3-540-42627-23rded.Springer-VerlagBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved

3、,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Dupli-cationofthispublicationorpartsthereofispermittedonlyunderthepro

4、visionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringeronline.com©Springer-VerlagBerlin

5、Heidelberg1995,1998,2001,2005PrintedinGermanyTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneralu

6、se.Typesetting:bytheauthorusingaSpringerLATEXmacropackageCoverdesign:ErichKirchner,HeidelbergPrintedonacid-freepaperSPIN1142254941/TechBooks-543210DedicatedtoShing-TungYau,forsomanydiscussionsaboutmathematicsandChineseculturePrefaceRiemanniangeometryischaracterized,

7、andresearchisorientedtowardsandshapedbyconcepts(geodesics,connections,curvature,...)andobjectives,inparticulartounderstandcertainclassesof(compact)Riemannianmanifoldsdefinedbycurvatureconditions(constantorpositiveornegativecurvature,...).Bywayofcontrast,geometricanal

8、ysisisaperhapssomewhatlesssystem-aticcollectionoftechniques,forsolvingextremalproblemsnaturallyarisingingeometryandforinvestigatingandchar