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1、ClassicalGeometriesinModernWalterBenzContextsGeometryofRealInnerProductSpacesBirkhäuserVerlagBasel•Boston•BerlinAuthors:WalterBenzFachbereichMathematikUniversitätHamburgBundesstr.5520146HamburgGermanye-mail:benz@math.uni-hamburg.de2000MathematicalSubjectClassification3
2、9B52,51B10,51B25,51M05,51M10,83C20ACIPcataloguerecordforthisbookisavailablefromtheLibraryofCongress,WashingtonD.C.,USABibliographicinformationpublishedbyDieDeutscheBibliothekDieDeutscheBibliothekliststhispublicationintheDeutscheNationalbibliografie;detailedbibliographi
3、cdataisavailableintheInternetat.ISBN3-7643-7371-7BirkhäuserVerlag,Basel–Boston–BerlinThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,r
4、ecitation,broadcast-ing,reproductiononmicrofilmsorinotherways,andstorageindatabanks.Foranykindofusepermissionofthecopyrightownermustbeobtained.©2005BirkhäuserVerlag,P.O.Box133,CH-4010Basel,SwitzerlandPartofSpringerScience+BusinessMediaCoverdesign:MichaLotrovsky,CH-4106
5、Therwil,SwitzerlandPrintedonacid-freepaperproducedfromchlorine-freepulp.TCF°°PrintedinGermanyISBN-10:3-7643-7371-7e-ISBN:3-7643-7432-2ISBN-13:978-3-7643-7371-9987654321www.birkhauser.chContentsPrefaceix1TranslationGroups11.1Realinnerproductspaces.......................
6、11.2Examples................................21.3Isomorphic,non-isomorphicspaces..................31.4InequalityofCauchy–Schwarz.....................41.5Orthogonalmappings.........................51.6Acharacterizationoforthogonalmappings..............71.7Translationgrou
7、ps,axis,kernel....................101.8Separabletranslationgroups......................141.9Geometryofagroupofpermutations.................161.10Euclidean,hyperbolicgeometry....................201.11Acommoncharacterization......................211.12Otherdirections,aco
8、unterexample..................342EuclideanandHyperbolicGeometry372.1Metricspaces..............................372.2Th
