标量曲率Finsler空间与Finsler度量的射影变换

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1、维普资讯http://www.cqvip.coml～og,g,1‘刁杂志．4J．ofMath．(PRC){liFINSLERSPACESOFSCALARCURVATUREANDilPROJECTIVECHANGESOFFINSLERMETRICS幸lCHENXin-yue(程新跃)l(Dept．ofMath,ChongqingInstituteofTechnology,Chongqing,400050)illAbstract：Inthispaper,westudytheFinslerspacesofsoghlrcurvaturewhicharepo

2、intwiselprojectivetoaFinslerspaceofRieci-tlat(i．e．theRiecicurvatureRic=0oraFinsler8paeeoflconstantcurvaturerespectively·We。btain8omesuficientandnsoesl~ryc。nclif。118underwhichlisuchFinslerspacesofsoghlrcurvaturebecometheFinslerspacesofconstantcurvature．Particularly，wegivesomeco

3、ndition8thataprojsotivelyflatFinslerSp~lCei8ofc。nsttmtcurvature．!Keywords：Finalerspace；Riccicurvature；projectivechange；Finslerspaceofconsttmtcurvature．20O0MRSubjectClassification：53C60；53C40Documenteode：AArticleIl1)：0255-7797(2003)04-0455-081IntroductionjFinslerprojectivegeome

4、tryisallimportantpartofFinslergeometryandhasbeenconsideredbysomegeometers，forexample，see【1】【4][5][61and[81[91．TworegularF~inl[nselergemodeetrsiccsasonpoainmtanseiftosldaresaidtobepointwiseprojectivelyrelatediftheyhavetheI．TworegularFinslermetricspacesaresaidtobeprojectivelyrel

5、atedifthereisdifeomo~hismbetweenthemsuchthatthepull-backmetricispointwiseprojectivetoanotherone．ItisthemostfundamentalthattheDouglastensorandtheWeyltensorareinvariantunderanyprojectivechange．AFinslerspaceiscailedprojectivelyflat,ifithasacoveringbycoordinateneighborhoodsinwhice

6、itisprojectiveitoalocallyMinkowskispaceorFinslermetricFispointwiseprojectivdyrelatedtoalocallyMinkowskimetric)．ItisshownthatFinslerspacesinwhichtheDouglastensorandtheWeyltenservanishsimultaneouslyareprojectivelyflat．Infact，aprojectivelyflatFinslerspaceis’Finslerspacewithrectil

7、ineargeodesics，whichWasoriginallysuggestedbyHilbert．、Ingeneral，givenaFinslermetriconamanifoldwewouldliketodetermineallFinslermetricswhicharepointwiseprojectivetothegivenone．Patticular]y,wewouldlike霹RFoemcemivleafldodnatitee：m20：S0Sc1uie-p-n0pc2oer--t0eF8doubnydaNtioatnioAonfac

8、lcCeNhpoatnetugrrqaiSlnegSpd／B~eda眦zcbelmeroFno3un0C,do2ma0ti