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:LetMbeapositivequaternionicKhlermanifoldofdimension4m.Wealreadyshowedthatifthesymmetryrankisgreaterthanorequalto[m/2]+2andthefourthBettinumberb_4isequaltoone,thenMisisometrictoHP~(m).Thegoalofthispaperistoreportthatwecanimprovethelowerboundofthesymmetryrankbyoneforhighereven-dimensionalpositivequaternionicKahlermanifolds.Namely,itisshowninthispaperthatifthesymmetryrankofMwithb_4(M)=1isgreaterthanorequaltom/2+1form≥10,thenMisisometrictoHP~m.OneofthemainstrategiesofthispaperistoapplyamoredelicateargumentofFrankeltypetopositivequaternionicKhlermanifoldswithcertainsymmetryrank.