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简介：<正>Foranyintegersa1,a2,a3,a4andcwitha1a2a3a40（modp）,thispapershowsthatthereexistsasolutionX=（x1,x2,x3,x4）∈Z4ofthecongruencea1x12+a2x22+a3x32+a4x42≡c（modp）suchthat‖X‖=max{|x1|,|x2|,|x3|,|x4|}《p1/2logp.

简介：让x：Mn是有非零主管弯曲的脐的免费hypersurface。然后，x与Laguerre公制的g被联系，Laguerre张肌\mathbbL\mathbb{L}，Laguerre形式C，和一个Laguerre秒基础形成\mathbbB\mathbb{B}它是在Laguerre下面的x的invariants转变组。如果它的Laguerre形式消失，hypersurfacex被称为Laguerreisoparametric并且\mathbbB\mathbb的特征值{B}是不变的。在这份报纸，我们在4分类所有Laguerreisoparametrichypersurfaces。

简介：Wegiveanestimateoftypesup×infonRiemannianmanifoldofdimension4foraYamabetypeequation.

简介：InthisarticlethespectrumofsupportsizesofacompletelydecomposableTS(ν,,4)foranypositiveintegerν≡1,3(mod6)isdetermined.

简介：设(M,T)是一个光滑闭流形上的对合,不动点集为F=RP(4)UP(4,2n-1),则它的每一个对合(M,T)必协边(RP(4)×RP(4),twist)和(P(4,2n),T')之一.

简介：设F24为实一阶李群—F4的一个实型式,我们用F4的weyl群来参数化F24的广义主系列表示,因此,我们可以利用[1]提出的方便和直接的方法对奇异无穷小特征来计算F24的广义主系列表示的组合因子。

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简介：Thispapergivesaclassificationofcompletehypersurfaceswithnonzeroconstantmeancurvatureandconstantquasi-Gauss-KroneckercurvatureinthehyperbolicspaceH4(-1),whosescalarcurvatureisboundedfrombelow.

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简介：<正>InthispaperwestudysurfacesinS~4andtheirtwistorGaussmaps.SomenecessaryandsufficientconditionsthatthetwistorGaussmapisharmonicaregiven.Wefindmanyexamplesofnonisotropicharmonicmapsfromasurfaceto(?)P~3.

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简介：Themainresultsareasfollows.

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简介：本文介绍了一个引理,这个引理奠定了K4-同胚图K4(α,1,1,δ,ε,η)色性研究的基础.

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简介：LetMbeapositivequaternionicKhlermanifoldofdimension4m.Wealreadyshowedthatifthesymmetryrankisgreaterthanorequalto[m/2]+2andthefourthBettinumberb_4isequaltoone,thenMisisometrictoHP~(m).Thegoalofthispaperistoreportthatwecanimprovethelowerboundofthesymmetryrankbyoneforhighereven-dimensionalpositivequaternionicKahlermanifolds.Namely,itisshowninthispaperthatifthesymmetryrankofMwithb_4(M)=1isgreaterthanorequaltom/2+1form≥10,thenMisisometrictoHP~m.OneofthemainstrategiesofthispaperistoapplyamoredelicateargumentofFrankeltypetopositivequaternionicKhlermanifoldswithcertainsymmetryrank.

简介：Inthispaper,acompleteclassificationofarc-transitivecubicgraphsoforder4pisgiven.

简介：Assumethatm≥2,pisaprimenumber,(m,p(p-1))=1,-1(Z/mZ)~*and[(Z/mZ)~*:]=4.Inthispaper,wecalculatethevalueofGausssumG(X)=Σ_(x∈F_q~*)x(x)ζ_p~(T(x))overF_q,whereq=p~f,f=((m))/4xisamultiplicativecharacterofF_qandTisthetracemapfromF_qtoF_p.Underourassumptions,G(x)belongstothedecompositionfieldKofpinQ(ζm)andKisanimaginaryquarticabeliannumberfield.WhentheGaloisgroupGal(K/Q)iscyclic,wehavestudiedthiscycliceaseinanotherpaper:'Gausssumsofindexfour:(1)cycliccase'(acceptedbyActaMathematicaSinica,2003).Inthispaperwedealwiththenon-cycliccase.