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1、UniversitextEditorialBoard(NorthAmerica):S.AxlerK.A.RibetThomasE.CecilLieSphereGeometryWithApplicationstoSubmanifoldsSecondEditionThomasE.CecilDepartmentofMathematicsandComputerScienceCollegeoftheHolyCross1CollegeStreetWorcester,MA01610cecil@mathcs.holycross.eduEditorialBoard(NorthAmerica
2、):S.AxlerK.A.RibetMathematicsDepartmentMathematicsDepartmentSanFranciscoStateUniversityUniversityofCaliforniaatBerkeleySanFrancisco,CA94132Berkeley,CA94720-3840USAUSAaxler@sfsu.eduribet@math.berkeley.eduISBN:978-0-387-74655-5e-ISBN:978-0-387-74656-2LibraryofCongressControlNumber:200793669
3、0MathematicsSubjectClassification(2000):53-02,53A07,53A40,53B25,53C40,53C42©2008SpringerScience+BusinessMedia,LLCAllrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMediaLLC,233SpringStreet,NewYork,NY10013,U.S
4、.A.),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,s
5、ervicemarksandsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaper.987654321springer.com(JLS/SB)Tomysons,Tom,Mark,andMichaelPrefacetotheFirstEditionThepurposeofthismonographistoprovidean
6、introductiontoLiesgeometryoforientedspheresanditsrecentapplicationstothestudyofsubmanifoldsofEuclideanspace.Lie[104]introducedhisspheregeometryinhisdissertation,publishedasapaperin1872,anduseditinhisstudyofcontacttransformations.Thesubjectwasactivelypursuedthroughtheearlypartofthetwentien
7、thcentury,culminatingwiththepublicationin1929ofthethirdvolumeofBlaschkes[10]VorlesungenüberDifferentialgeometrie,whichisdevotedentirelytoLiespheregeometryanditssubgeometries.Afterthis,thesubjectfelloutoffavoruntil1981,whenPinkall[146]useditastheprincipaltoolinhiscla
