SUBMANIFOLDS OF PRODUCT RIEMANNIAN MANIFOLD

1IntroductionLetUandVbeRiemannianmanffolds,withthedimensionn1andn2respectively.UxVistheRiemannianproductofUandV.WedenotebyPandQtheprojectionmappingsofT(UxV)toTUaildTVrespectively.ThenwehaveWeputJ=P-Q.ItiseasytoseethatJ~=I.WedefineaRiemannianmetricofUxVbyg(X,Y)==g1(PX,PY) g2(QX,QY),wllereg1andg2areRiemannia11metricofUandVrespectively.ItfollowsthatBy7wedellotetheg'sLevi-Civitaconnection.ThenwecaneasilyseethatInfact,Frollltlledefillitiollofg,wecangetthatUalldVareallgeodesicsub…     

整体Poincaré受截面存在性的拓扑障碍(英文)

本文讨论了流形上流的整体Poincare截面的存在性。并证明了流形的一般拓扑导致整体Poincare截面的存在性的障碍。     

紧致极小超曲面上Laplace算子的谱

设M为S~(pn 1)中紧致极小超曲面，M_(p，n-p)为S~(pn 1)的Clifford极小超曲面，若Spec（M）=Spec（M_(p,n-p)），在一定条件下，我们可以得出M与M_(p,n-p)等距同构．     

THE SPECTRUM OF THE LAPLACE OPERATION ON COMPACT SUBMANIFOLDS

1IntroductionLetiM.g)beac0mpactn-dimensi0nd1Riemannianmanffold.ByAwedenotetheLaplacianartingonpf0rnaonM.Thenwehavethespectrumforeachp:Oneoftlieprob1emonspectraisasf0110ws:Let(M,g)and(M,g)becompactoritabieRicmannianmanif01dswithSpecp(M.g)=Specp{M-g),thenis(M,g)isometricto(M-j)?Thisprob1emisprovedtobewrongbyJ.Milnorin1964.Butwhen(M,g)and(M.g)aresonlespecialffiemannianmanifolds.undercertainconditi0ns.wecanprovethat(M.g)'sisometricto{M.j).Foran-din1ensi0nsubmanitbldMinSN,wedenotetheleng…